Download presentation
Presentation is loading. Please wait.
Published byBerenice Eaton Modified over 9 years ago
1
Warm Up 11.09.11 Week 4 Describe what each acronym means: 1) AAA2) AAS 3) SSA4) ASA
2
Geometry 4.4 Day 1 I will prove that triangles are congruent using the ASA and AAS Postulates. ASA - Angle Side Angle Congruence If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent. Postulate 21 ∆ABC ≅ ∆DEF because of ASA. ∠ A ≅ ∠ D ∠ C ≅ ∠ F ≅ C A B F D E
3
AAS - Angle Angle Side Congruence If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. Theorem 4.5 ∆ABC ≅ ∆DEF because of AAS. C A B F D E ∠ A ≅ ∠ D ∠ C ≅ ∠ F ≅ If, and, then
4
StatementReason Ex 1 C A B F D E ∠ A ≅ ∠ D Given ∠ C ≅ ∠ F Given ∠ B ≅ ∠ E Third Angle Theorem (4.3) Prove Theorem 4.5: ∆ABC ≅ ∆DEF: ∆ABC ≅ ∆DEF ASA ( P21 ) ≅
5
is given. is given because of AAS. ∠ E ≅ ∠ J ∆EFG ≅ ∆JHG Ex 2 Prove ∆EFG ≅ ∆JHG: E F G H J ≅ are vertical angles. ∠ EGF ≅ ∠ JGH
6
Ex 3 Prove ∆ABD ≅ ∆EBC: C B A D E StatementReason ≅ Given ∥ ∠ D ≅ ∠ C Alternate Interior Angles Theorem (3.8) ∠ ABD ≅ ∠ EBC Vertical Angles Theorem (2.6) ∆ABD ≅ ∆EBCASA
7
Do: 1 Assignment: Textbook Page 223, 8 - 22 all. Is ∆NQM ≅ ∆PMQ? Give congruency statements to prove it. N Q P M
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.