* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lesson 11.2 - Congruent Triangles
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
Multilateration wikipedia , lookup
Golden ratio wikipedia , lookup
History of geometry wikipedia , lookup
Penrose tiling wikipedia , lookup
Technical drawing wikipedia , lookup
Euler angles wikipedia , lookup
Rational trigonometry wikipedia , lookup
Apollonian network wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Lesson 11.2 - Congruent Triangles We will develop criteria for proving triangle congruence and I will determine which congruence criteria can be used to show that two triangles are congruent. October 31, 2016 There are five combinations of three congruent parts that suggest that two triangles are identical. List the five different combinations that seem to guarantee that two triangles are congruent. These combinations are called congruent triangle methods. SSS SAS ASA AAS HL SSS - Side-Side-Side Congruence Postulate: If 3 sides of one triangle are congruent to 3 sides of another, then the 2 triangles are congruent. B A A C P M Congruence Statement - ΔABC ΔMAP SAS - Side-Angle-Side Congruence Postulate: If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another, then the 2 triangles are congruent. B A U C N F Congruency Statement - ΔABC ΔFUN ASA - Angle-Side-Angle Congruence Postulate: If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another, then the 2 triangles are congruent. B A Y C X Z Congruency Statement - ΔABC ΔZYX AAS - Angle-Angle-Side Congruence Theorem: If 2 angles and a non-included side of one triangle are congruent to 2 angles and a nonincluded side of another, then the 2 triangles are congruent. B A Y C X Congruency Statement - ΔABC ΔZYX Z Are the triangles congruent? If so, write the congruence statement and state the reason (postulate). 1. U V 2. B Y Not enough info. SSS X W C ∆UVX ∆WVX Z D A 3. A C A 4. B B N L A D C M B Hint: Redraw by pulling triangles apart. Yes. ABC MLN SAS Yes. ABC DCB SAS C B BC BC D C