https://www.khanacademy.org/math/mr-class-10/x5cfe2ca097f0f62c:similarity/x5cfe2ca097f0f62c:theorem-of-area-of-similar-triangles/v/areas-of-similar-triangles 2025-10-27T13:00:49.737051923Z Areas of similar triangles In this video, we dive into the fascinating world of similar triangles and uncover a powerful geometric relationship: the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. You'll see a clear, step-by-step proof of this theorem, starting from visual intuition and building up to formal reasoning, followed by a practice problem to help solidify your understanding. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 00:42 Proof of Areas of similar triangles theorem 04:28 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 Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Areas of similar triangles In this video, we dive into the fascinating world of similar triangles and uncover a powerful geometric relationship: the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. You'll see a clear, step-by-step proof of this theorem, starting from visual intuition and building up to formal reasoning, followed by a practice problem to help solidify your understanding. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 00:42 Proof of Areas of similar triangles theorem 04:28 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 Khan Academy https://cdn.kastatic.org/ka-youtube-converted/qwx1_nNaPNo.mp4/qwx1_nNaPNo.mp4 331 Ratio and Proportion in Geometry https://www.khanacademy.org/math/mr-class-10/x5cfe2ca097f0f62c:similarity/x5cfe2ca097f0f62c:basic-proportionality-theorem/v/basic-proportionality-theorem 2025-10-06T14:00:44.591197305Z Basic Proportionality Theorem In this video, we begin with a hands-on activity to intuitively explore the Basic Proportionality Theorem (BPT), also known as Thales’ Theorem. Using simple materials and visual setups, we experimentally verify how a line drawn parallel to one side of a triangle divides the other two sides in the same ratio. Once the concept feels concrete, we transition to a formal mathematical proof, connecting observation with logic. This blend of experiment and reasoning helps learners truly grasp why BPT works—and sets the stage for applying it confidently in geometry problems. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 An activity to understand BPT 03:10 Proof of BPT 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 Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Basic Proportionality Theorem In this video, we begin with a hands-on activity to intuitively explore the Basic Proportionality Theorem (BPT), also known as Thales’ Theorem. Using simple materials and visual setups, we experimentally verify how a line drawn parallel to one side of a triangle divides the other two sides in the same ratio. Once the concept feels concrete, we transition to a formal mathematical proof, connecting observation with logic. This blend of experiment and reasoning helps learners truly grasp why BPT works—and sets the stage for applying it confidently in geometry problems. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 An activity to understand BPT 03:10 Proof of BPT 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 Khan Academy https://cdn.kastatic.org/ka-youtube-converted/94IRgatBRjM.mp4/94IRgatBRjM.mp4 414 Ratio and Proportion in Geometry https://www.khanacademy.org/math/mr-class-10/x5cfe2ca097f0f62c:similarity/x5cfe2ca097f0f62c:basic-proportionality-theorem/v/converse-of-basic-proportionality-theorem 2025-10-06T14:00:44.591197305Z Converse of Basic Proportionality Theorem In this engaging math video, we explore the Converse of the Basic Proportionality Theorem—starting with a hands-on activity that visually demonstrates how the converse works in action. Through intuitive diagrams and real-time exploration, learners discover the proportional relationships that hint at parallel lines. Once the concept clicks, we transition to a formal proof, showing how logical reasoning confirms what the activity revealed. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 What is converse of BPT 00:50 An activity on converse of BPT 05:36 Prrof of converse of BPT 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 Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Converse of Basic Proportionality Theorem In this engaging math video, we explore the Converse of the Basic Proportionality Theorem—starting with a hands-on activity that visually demonstrates how the converse works in action. Through intuitive diagrams and real-time exploration, learners discover the proportional relationships that hint at parallel lines. Once the concept clicks, we transition to a formal proof, showing how logical reasoning confirms what the activity revealed. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 What is converse of BPT 00:50 An activity on converse of BPT 05:36 Prrof of converse of BPT 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 Academy https://cdn.kastatic.org/ka-youtube-converted/fnNmdmCwihE.mp4/fnNmdmCwihE.mp4 503 Ratio and Proportion in Geometry https://www.khanacademy.org/math/revision-term-1-mh-math-class-10/x041ca11815640a3a:week-1/x041ca11815640a3a:similarity/e/basic-proportionality-theorem-problems 2025-12-30T07:05:15.972746521Z Basic proportionality theorem problems The exercise tests how students can identify missing lengths by applying basic proportionality theorem and its converse Devashish Phadnis exercise https://www.khanacademy.org/math/revision-term-1-mh-math-class-10/x041ca11815640a3a:week-1/x041ca11815640a3a:similarity/e/converse-of-bpt 2026-04-07T23:17:37.123726494Z Converse of BPT Converse of BPT Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-mh-math-class-10/x041ca11815640a3a:week-1/x041ca11815640a3a:similarity/e/three-parallel-lines-and-their-transversals 2026-04-08T01:15:04.085520103Z Three parallel lines and their transversals Three parallel lines and their transversals Ashish Gupta exercise