https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pythagorean-proofs/v/pythagorean-theorem-proof-using-similarity 2020-11-15T14:51:29Z Pythagorean theorem proof using similarity Proof of the Pythagorean Theorem using similarity Sal Khan video https://cdn.kastatic.org/googleusercontent/G8PP6NVPqmX4eEb2CQ-DK0mbTqzwTTJbBPXMyGG96LfV7Pinvaeysovn_3QY8yNDOZ9cldIZCpAB_j2wUIcvWsRV Pythagorean theorem proof using similarity Proof of the Pythagorean Theorem using similarity https://cdn.kastatic.org/ka-youtube-converted/LrS5_l-gk94.mp4/LrS5_l-gk94.mp4 592 Proving relationships using similarity https://www.khanacademy.org/math/geometry/hs-geo-similarity/xff63fac4:hs-geo-proving-relationships-using-similarity/v/exploring-medial-triangles 2021-04-21T12:03:02Z Exploring medial triangles The three midsegments (segments joining the midpoints of the sides) of a triangle form a medial triangle. Find out the properties of the midsegments, the medial triangle and the other 3 triangles formed in this way. Sal Khan video https://cdn.kastatic.org/googleusercontent/LVJ6ro_jdgfVM67FNz-1vT__NgvQZEdNdgwKKTKAyqFYQ8uNKdND9hPuxplQLo0N90lx2xNWnWJo7pV-yQobDAQ Exploring medial triangles The three midsegments (segments joining the midpoints of the sides) of a triangle form a medial triangle. Find out the properties of the midsegments, the medial triangle and the other 3 triangles formed in this way. https://cdn.kastatic.org/ka-youtube-converted/Rsi5mzEaCPw.mp4/Rsi5mzEaCPw.mp4 693 Proving relationships using similarity https://www.khanacademy.org/math/geometry/hs-geo-similarity/xff63fac4:hs-geo-proving-relationships-using-similarity/v/proof-parallel-lines-divide-triangle-sides-proportionally 2022-09-10T02:03:40.164764806Z Proof: Parallel lines divide triangle sides proportionally Prove that a line parallel to one triangle side divides other sides proportionately. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/c273ba7a-5ccb-4b29-aa52-b48409cc210a_1280_720_base.png Proof: Parallel lines divide triangle sides proportionally Prove that a line parallel to one triangle side divides other sides proportionately. https://cdn.kastatic.org/ka-youtube-converted/L1c0SP4W4ro.mp4/L1c0SP4W4ro.mp4 392 Proving relationships using similarity 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/geometry/hs-geo-similarity/xff63fac4:hs-geo-proving-relationships-using-similarity/v/similar-triangles-to-prove-that-the-slope-is-constant-for-a-line 2021-02-16T16:08:13Z Proving slope is constant using similarity Sal uses a clever proof involving similar triangles to show that slope is constant for a line. Sal Khan video https://cdn.kastatic.org/googleusercontent/4g4avn3hfPfOyNuoxKRO3Y9JEnZYFAmrxj1QpH9HngPpSYZI5kSuz6B9DVGXpNmLrYRFTlBATZbVkAO2OHRvO9tm Proving slope is constant using similarity Sal uses a clever proof involving similar triangles to show that slope is constant for a line. https://cdn.kastatic.org/ka-youtube-converted/24WMbh1BBKc.mp4/24WMbh1BBKc.mp4 476 Proving relationships using similarity https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/proving-that-parallel-lines-have-the-same-slope 2022-10-07T00:00:24.225559754Z Proof: parallel lines have the same slope Sal proves that parallel lines have the same slope using triangle similarity. video https://cdn.kastatic.org/ka_thumbnails_cache/7e99591f-b908-4ab3-aa98-39b92da11e67_1280_720_base.png Proof: parallel lines have the same slope Sal proves that parallel lines have the same slope using triangle similarity. https://cdn.kastatic.org/ka-youtube-converted/9ZYoIliBXYE.mp4/9ZYoIliBXYE.mp4 349 Proving relationships using similarity https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/proof-that-perpendicular-lines-have-negative-reciprocal-slope 2023-05-12T21:01:01.897246564Z Proof: perpendicular lines have opposite reciprocal slopes To prove that perpendicular lines have opposite reciprocal slopes, draw the two lines and label key points. By identifying the two right triangles that are formed, one can use the definition of slope to calculate the slopes of the two lines. Finally, using the properties of similar right triangles, show that the two slopes are indeed opposite reciprocals of each other. video https://cdn.kastatic.org/ka_thumbnails_cache/2bc66806-665b-4fd9-b916-90c0d1722d9f_1280_720_base.png Proof: perpendicular lines have opposite reciprocal slopes To prove that perpendicular lines have opposite reciprocal slopes, draw the two lines and label key points. By identifying the two right triangles that are formed, one can use the definition of slope to calculate the slopes of the two lines. Finally, using the properties of similar right triangles, show that the two slopes are indeed opposite reciprocals of each other. https://cdn.kastatic.org/ka-youtube-converted/HyThzLRuqXo.mp4/HyThzLRuqXo.mp4 535 Proving relationships using similarity