https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/a/properties-of-congruence-and-equality 2024-08-02T18:09:52.444389438Z Properties of congruence and equality Learn when to apply the reflexive property, transitive, and symmetric properties in geometric proofs. Learn the relationship between equal measures and congruent figures. article https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180 2023-05-12T21:01:01.897246564Z Angles in a triangle sum to 180° proof The sum of the interior angle measures of a triangle always adds up to 180°. We can draw a line parallel to the base of any triangle through its third vertex. Then we use transversals, vertical angles, and corresponding angles to rearrange those angle measures into a straight line, proving that they must add up to 180°. Sal Khan video https://cdn.kastatic.org/googleusercontent/-_9m7sXFJ_DZGRlkqOTzZjy4vuXCY0hC1HrMevIJscQ5fyFoU8mekOV5C99_DXZ89kc-lHRN1rhn4WhPlCY4svU Angles in a triangle sum to 180° proof The sum of the interior angle measures of a triangle always adds up to 180°. We can draw a line parallel to the base of any triangle through its third vertex. Then we use transversals, vertical angles, and corresponding angles to rearrange those angle measures into a straight line, proving that they must add up to 180°. https://cdn.kastatic.org/ka-youtube-converted/6s1CI3uuhko.mp4/6s1CI3uuhko.mp4 268 Theorems concerning triangle properties https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/congruent-legs-and-base-angles-of-isosceles-triangles 2021-02-16T16:08:13Z Proofs concerning isosceles triangles Sal proves that the base angles in isosceles triangles are congruent, and conversely, that triangles with congruent base angles are isosceles. He also proves that the perpendicular to the base of an isosceles triangle bisects it. Sal Khan video https://cdn.kastatic.org/googleusercontent/jEEfJHzFh50C2S_kmU9OCZKaxDbUeLZIoYZkeTy7-8xRyagY_ZkNjJ-ozLt80fhqzLRu8mhn-5yvYZKC43gfD3Xy Proofs concerning isosceles triangles Sal proves that the base angles in isosceles triangles are congruent, and conversely, that triangles with congruent base angles are isosceles. He also proves that the perpendicular to the base of an isosceles triangle bisects it. https://cdn.kastatic.org/ka-youtube-converted/7UISwx2Mr4c.mp4/7UISwx2Mr4c.mp4 543 Theorems concerning triangle properties https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/equilateral-triangle-sides-and-angles-congruent 2021-02-16T16:08:14Z Proofs concerning equilateral triangles Sal proves that the angles of an equilateral triangle are all congruent (and therefore they all measure 60°), and conversely, that triangles with all congruent angles are equilateral. Sal Khan video https://cdn.kastatic.org/googleusercontent/QZ8jOQF11Eu-j3PcjFZSdaTq-lwCZ6mvoESc1Nv7ewc_iNlTMDB0BhS4Mzs2690ta8FsShYI4_IxL0-nJN-RywQJ Proofs concerning equilateral triangles Sal proves that the angles of an equilateral triangle are all congruent (and therefore they all measure 60°), and conversely, that triangles with all congruent angles are equilateral. https://cdn.kastatic.org/ka-youtube-converted/CYNUwiUzlPk.mp4/CYNUwiUzlPk.mp4 389 Theorems concerning triangle properties https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/triangle-angle-example-1 2023-06-02T19:09:07.369858129Z Triangle exterior angle example An exterior angle is formed outside a triangle by extending a side. Its measure is equal to the sum of the two non-adjacent interior angle measures, thanks to the fact that all angle measures in a triangle add up to 180 degrees. Sal Khan video https://cdn.kastatic.org/googleusercontent/wLp2r0BNUUczDRaf0FEYElR-f16JqkKrGUXqmRV93k5fLjL3OY9okjdUz_do9oPMYQ6F7w7Q2DEqiHXfD9snNWDTPQ Triangle exterior angle example An exterior angle is formed outside a triangle by extending a side. Its measure is equal to the sum of the two non-adjacent interior angle measures, thanks to the fact that all angle measures in a triangle add up to 180 degrees. https://cdn.kastatic.org/ka-youtube-converted/hmj3_zbz2eg.mp4/hmj3_zbz2eg.mp4 363 Theorems concerning triangle properties https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/e/prove-triangle-properties 2026-05-06T17:00:53.280539768Z Prove triangle properties Use transformations, line and angle relationships, and triangle congruence criteria to prove properties of triangles. Charlotte Auen exercise