https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors/v/constructing-a-perpendicular-bisector-using-a-compass-and-straightedge 2021-02-16T16:08:13Z Geometric constructions: perpendicular bisector Sal constructs a perpendicular bisector to a given line segment using compass and straightedge. Sal Khan video https://cdn.kastatic.org/googleusercontent/Bjfj2eM1niFGunZY-P1N3CxVS8HNTbRplbz-yjCosmkaJsSoTSa0ZldRXgPIS1fvnMhp540o38QZpOuL7RA2JUg Geometric constructions: perpendicular bisector Sal constructs a perpendicular bisector to a given line segment using compass and straightedge. https://cdn.kastatic.org/ka-youtube-converted/WR2R_wrdEVY.mp4/WR2R_wrdEVY.mp4 86 Triangle and triangle inequality theorems https://www.khanacademy.org/math/math-1-illustrative-math-aligned/x193529144fa1e1f6:congruence/x193529144fa1e1f6:the-perpendicular-bisector-theorem/a/perpendicular-bisector-theorem 2026-03-27T16:26:41.85316871Z Perpendicular bisector theorem Prove the Perpendicular Bisector Theorem and its converse. article https://www.khanacademy.org/math/9th-grade-math-revised-k-to-10-3-terms/x1e64c39423990571:3rd-quarter/x1e64c39423990571:triangle-and-triangle-inequality-theorems/e/perpendicular-bisector 2026-06-01T10:00:48.582989644Z Perpendicular bisector This exercise helps students understand the properties and construction of the perpendicular bisector of a line segment using geometric reasoning, paper folding, and compass constructions. Khan Academy exercise https://www.khanacademy.org/math/revision-term-1-mh-math-class-7/x0bdc8a5f9d8ec377:week-1/x0bdc8a5f9d8ec377:geometrical-constructions/e/property-of-perpendicular-bisectors-of-a-triangle 2026-04-08T00:36:09.500768563Z Property of perpendicular bisectors of a triangle Property of perpendicular bisectors of a triangle Ashish Gupta exercise https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-angle-bisector-theorem/v/angle-bisector-theorem-proof 2023-06-02T18:07:10.327662797Z Intro to angle bisector theorem The Angle Bisector Theorem states that when an angle in a triangle is split into two equal angles, it divides the opposite side into two parts. The ratio of these parts will be the same as the ratio of the sides next to the angle. Sal Khan video https://cdn.kastatic.org/googleusercontent/GyWsCYqbdq87zseUd2Adqrb92DCxxWgAL5dkofP4-PHA93Zu3VMq0rXdV_B5Uprw_XZginA4uninZfDjiZY1j2Y Intro to angle bisector theorem The Angle Bisector Theorem states that when an angle in a triangle is split into two equal angles, it divides the opposite side into two parts. The ratio of these parts will be the same as the ratio of the sides next to the angle. https://cdn.kastatic.org/ka-youtube-converted/TpIBLnRAslI.mp4/TpIBLnRAslI.mp4 515 Triangle and triangle inequality theorems https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors/v/constructing-an-angle-bisector-using-a-compass-and-straightedge 2021-02-16T16:08:13Z Geometric constructions: angle bisector Sal constructs a line that bisects a given angle using compass and straightedge. Sal Khan video https://cdn.kastatic.org/googleusercontent/k0ShVOtWKk8bpYbdkwztYCR_s299KJ7K2IC6cbiEn3WNlW88vonoAm9h67WtxvGHEFGXes-Y5in6opSJHr702xMy Geometric constructions: angle bisector Sal constructs a line that bisects a given angle using compass and straightedge. https://cdn.kastatic.org/ka-youtube-converted/KNr52iFk7n4.mp4/KNr52iFk7n4.mp4 137 Triangle and triangle inequality theorems https://www.khanacademy.org/math/revision-term-1-mh-math-class-7/x0bdc8a5f9d8ec377:week-1/x0bdc8a5f9d8ec377:geometrical-constructions/e/property-of-angle-bisectors-of-a-triangle 2026-04-07T22:59:30.107127435Z Property of angle bisectors of a triangle Property of angle bisectors of a triangle Ashish Gupta exercise https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-angle-bisector-theorem/e/angle_bisector_theorem 2025-02-27T12:31:05.94748833Z Solve triangles: angle bisector theorem Use the angle bisector theorem to find missing side lengths in triangles. Igor Terzic exercise https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:quadrilaterals/x06d55bfa213a79fd:the-midpoint-theorem/v/midpoint-theorem 2025-05-21T09:59:19.381663781Z Midpoint theorem Dive into the mid-point theorem in this comprehensive video! Understand the theorem which states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half its length. Learn its proof step-by-step, supported by clear visuals and reasoning. To reinforce your understanding, tackle a practical example problem and see how the theorem is applied in real scenarios. Perfect for mastering this essential geometry concept! Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/math/ncert-class-9/x2757d6348a04b24e:quadrilaterals-ncert-new Timestamps: 0:00lntroduction 02:02 Proof of mid-point theorem 06:09 Practice Question Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by MAHAK WASAN Mahak Wasan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Midpoint theorem Dive into the mid-point theorem in this comprehensive video! Understand the theorem which states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half its length. Learn its proof step-by-step, supported by clear visuals and reasoning. To reinforce your understanding, tackle a practical example problem and see how the theorem is applied in real scenarios. Perfect for mastering this essential geometry concept! Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! https://www.khanacademy.org/math/ncert-class-9/x2757d6348a04b24e:quadrilaterals-ncert-new Timestamps: 0:00lntroduction 02:02 Proof of mid-point theorem 06:09 Practice Question Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by MAHAK WASAN https://cdn.kastatic.org/ka-youtube-converted/gutMr88XPcE.mp4/gutMr88XPcE.mp4 403 Triangle and triangle inequality theorems https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:quadrilaterals/x06d55bfa213a79fd:the-midpoint-theorem/e/midpoint-theorem 2026-05-12T22:10:47.015864082Z Midpoint theorem This exercise is curated for new ncert, midpoint theorem lesson in parallelograms and the problems are taken from Quadrilaterals 8.2 Devashish Phadnis exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem 2023-05-23T10:21:00.469536483Z Intro to the Pythagorean theorem The Pythagorean theorem is a cornerstone of math that helps us find the missing side length of a right triangle. In a right triangle with sides A, B, and hypotenuse C, the theorem states that A² + B² = C². The hypotenuse is the longest side, opposite the right angle. Sal Khan video https://cdn.kastatic.org/googleusercontent/zm9lxg5aZkInLh29lDFE0ccgsSaxlQuzX0ogkP6IbAwcTeapeXzOpPLaFNmpA6WAoS_PhTCuQDrDMou_Wqr5Y4nf Intro to the Pythagorean theorem The Pythagorean theorem is a cornerstone of math that helps us find the missing side length of a right triangle. In a right triangle with sides A, B, and hypotenuse C, the theorem states that A² + B² = C². The hypotenuse is the longest side, opposite the right angle. https://cdn.kastatic.org/ka-youtube-converted/AA6RfgP-AHU.mp4/AA6RfgP-AHU.mp4 646 Triangle and triangle inequality theorems https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/pythagorean-theorem-2 2023-05-23T10:21:00.469536483Z Pythagorean theorem example The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). We can apply the theorem to find the missing side length of a right triangle, even when the missing length is one of the shorter sides. Sal Khan video https://cdn.kastatic.org/googleusercontent/XK32AoBZRozQUpZpJZzO8wJ8dubmK4CBTp2rLWlJZZ1yp0lA38Fb8jbNDKgET_aGDhKN3AP6t7rikDHupKmPUbY Pythagorean theorem example The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). We can apply the theorem to find the missing side length of a right triangle, even when the missing length is one of the shorter sides. https://cdn.kastatic.org/ka-youtube-converted/O64YFlX1_aI.mp4/O64YFlX1_aI.mp4 257 Triangle and triangle inequality theorems https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/a/pythagorean-theorem-intro 2026-03-05T15:00:48.060394873Z Pythagorean theorem intro problems Practice using the Pythagorean theorem to solve for missing side lengths on right triangles.  Each question is slightly more challenging than the previous. article https://www.khanacademy.org/math/9th-grade-math-revised-k-to-10-3-terms/x1e64c39423990571:3rd-quarter/x1e64c39423990571:triangle-and-triangle-inequality-theorems/e/b9-pythagoras-theorem 2026-04-08T00:54:09.631945657Z Pythagoras theorem Pythagoras theorem ashish exercise https://www.khanacademy.org/math/9th-grade-math-revised-k-to-10-3-terms/x1e64c39423990571:3rd-quarter/x1e64c39423990571:triangle-and-triangle-inequality-theorems/e/pythagoras-theorem-triangles 2026-06-01T10:00:48.582989644Z Pythagoras Theorem - Triangles Pythagoras Theorem - Triangles Ashish Gupta exercise https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pyth-theorem/e/pythagorean-theorem-word-problems 2026-04-07T22:59:30.107127435Z Pythagorean theorem challenge Solve real-world problems that can be modeled by right triangles, using the Pythagorean Theorem! elizabeth exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/v/pythagorean-theorem-3 2023-06-02T19:09:07.369858129Z Pythagorean theorem word problem: carpet If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. Sal Khan video https://cdn.kastatic.org/googleusercontent/yu5zzccGvx1c9EkgqD5u-SX3Qt42CJ2BRnvfLfSYtExN8xzpTmsAD64vGZz5qoGjBvup3ST8TRsu258UWRd_mF0 Pythagorean theorem word problem: carpet If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. https://cdn.kastatic.org/ka-youtube-converted/T0IOrRETWhI.mp4/T0IOrRETWhI.mp4 180 Triangle and triangle inequality theorems https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/v/pythagorean-theorem-1 2023-06-02T19:09:07.369858129Z Pythagorean theorem word problem: fishing boat If we assume that the mast of a boat is at a right angle to the deck, then we can model the length of a rope stretched between the mast and deck as the hypotenuse of a right triangle. Then we can use the Pythagorean theorem to relate the lengths. Sal Khan video https://cdn.kastatic.org/googleusercontent/22gCRD837Vkb33-KqU1EhKn7rrhfmSAOggXycJrnLu-4ybDkIdPgF5UamYIBtD50PDrdaiCJkz0Qod7i2HU-JJX1nQ Pythagorean theorem word problem: fishing boat If we assume that the mast of a boat is at a right angle to the deck, then we can model the length of a rope stretched between the mast and deck as the hypotenuse of a right triangle. Then we can use the Pythagorean theorem to relate the lengths. https://cdn.kastatic.org/ka-youtube-converted/JVrkLIcA2qw.mp4/JVrkLIcA2qw.mp4 272 Triangle and triangle inequality theorems https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/e/pythagorean-theorem-word-problems--basic 2026-03-31T14:59:02.026924717Z Pythagorean theorem word problems Use the Pythagorean theorem to solve word problems. Lindsay exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-constructing-geometric-shapes/v/constructing-triangles-with-constraints 2021-06-30T20:49:37Z Construct a triangle with constraints Here's a challenge: in this problem we are given constraints and asked to construct a triangle. It can be done! You'll learn about degenerate triangles, too. Sal Khan video https://cdn.kastatic.org/googleusercontent/8QJGN2mqMMqvYB8ggWc1XozqdQaRPF-AHhMHiAkYM_hDxwOJ8p5DYL3UVFenVO639rtOnY9WDn0xyfYpaNF5XjOF Construct a triangle with constraints Here's a challenge: in this problem we are given constraints and asked to construct a triangle. It can be done! You'll learn about degenerate triangles, too. https://cdn.kastatic.org/ka-youtube-converted/E78ji1uBtSA.mp4/E78ji1uBtSA.mp4 239 Triangle and triangle inequality theorems https://www.khanacademy.org/math/geometry/hs-geo-similarity/xff63fac4:hs-geo-proving-relationships-using-similarity/e/prove-length-theorems-using-similarity 2026-05-12T18:20:39.36577347Z Prove theorems using similarity Using similarity, we can prove the Pythagorean theorem and theorems about segments when a line intersects 2 sides of a triangle. exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-constructing-geometric-shapes/v/triangle-inqequality-theorem 2021-07-02T09:35:27Z Triangle inequality theorem Intuition behind the triangle inequality theorem Sal Khan video https://cdn.kastatic.org/googleusercontent/HVpDfgDPIvUqFIbXtljJrLuUlHyeiWRomrkj6JeKGb5TPNgSbX0u_nX0Aj7RYaPpLreDkNourl80NDiBdD8tPeQ Triangle inequality theorem Intuition behind the triangle inequality theorem https://cdn.kastatic.org/ka-youtube-converted/KlKYvbigBqs.mp4/KlKYvbigBqs.mp4 352 Triangle and triangle inequality theorems https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:a-tale-of-three-intersecting-lines/x063f95a40c290960:properties-of-triangles-part-1/v/triangle-inequality-using-circle 2026-04-23T05:30:33.127061057Z Triangle inequality using circle Triangle inequality is one of the most fundamental concepts in geometry, and in this lesson we bring it to life through circle constructions. Starting with a quick recall of the triangle inequality, the video then explores how circles can be used to visualize and understand this property in a clear, intuitive way. You’ll see three distinct cases unfold—when circles intersect, when they just touch each other, and when they do not intersect at all—each offering a unique perspective on why the triangle inequality holds true. By the end, the conclusion ties these visualizations together, helping students grasp the concept not just logically, but visually and concretely. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Triangle inequality using circle Triangle inequality is one of the most fundamental concepts in geometry, and in this lesson we bring it to life through circle constructions. Starting with a quick recall of the triangle inequality, the video then explores how circles can be used to visualize and understand this property in a clear, intuitive way. You’ll see three distinct cases unfold—when circles intersect, when they just touch each other, and when they do not intersect at all—each offering a unique perspective on why the triangle inequality holds true. By the end, the conclusion ties these visualizations together, helping students grasp the concept not just logically, but visually and concretely. https://cdn.kastatic.org/ka-youtube-converted/V_Dsl8d5pqE.mp4/V_Dsl8d5pqE.mp4 333 Triangle and triangle inequality theorems https://www.khanacademy.org/math/9th-grade-math-revised-k-to-10-3-terms/x1e64c39423990571:3rd-quarter/x1e64c39423990571:triangle-and-triangle-inequality-theorems/e/b9-triangle-inequality 2026-04-07T23:17:37.123726494Z Triangle inequality Triangle inequality ashish exercise https://www.khanacademy.org/math/9th-grade-math-revised-k-to-10-3-terms/x1e64c39423990571:3rd-quarter/x1e64c39423990571:triangle-and-triangle-inequality-theorems/e/triangle-inequality-constructions 2025-05-28T21:38:23.633815025Z Triangle inequality theorem Use geometric constructions to justify why the length of the third side of a triangle must be greater than the difference of the lengths of the other sides and less than the sum of the lengths of the other sides. Charlie Auen exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-constructing-geometric-shapes/e/triangle_inequality_theorem 2025-10-14T14:00:50.911555133Z Triangle side length rules Given the lengths of two sides of a triangle, what can we say about the third side? Igor Terzic exercise