1. 4.2 APPLY CONGRUENCE AND TRIANGLES

2. What are congruent figures?
Same size, same shape. In a figure, corresponding sides and corresponding angles are congruent.

3. What are congruent figures?
Same size, same shape. In a figure, corresponding sides and corresponding angles are congruent. Ex. Congruent Not Congruent

4. Congruence statements
When you write a congruence statement for two polygons, always list the corresponding vertices in the same order. EX. B E A C D F

5. Congruence statements
EX.
ABC ≅ DEF B E A C D F

6. Congruence statements
EX.
Corresponding angles:
< A ≅ < D < B ≅ < E < C ≅ < F B E A C D F

7. Congruence statements
EX.
Corresponding sides:
AB ≅ DE BC ≅ EF AC ≅ DF B E A C D F

8. EX. ABCD ≅ EFGH Find x and y.
(2y – 4) FT B C E H
102O
(2x-8) O
84O
68O D A F G
8 FT

9. If <A ≅ <D and <B ≅ <E, Then <C ≅ <F
Third ANGLES THEOREM
If two angles of one triangle are congruent to two angles of another triangle, Then the third angles are also congruent.
If <A ≅ <D and <B ≅ <E, Then <C ≅ <F B E A C D F

10. EX. PTS ≅ RTQ Find <S and m<R.
68O Q S
75O T R

11. Properties of congruent triangles
Reflexive Property of Congruent Triangles For any triangle ABC, ABC ≅ ABC
Symmetric Property of Congruent Triangles If ABC ≅ DEF, then DEF ≅ ABC
Transitive Property of Congruent Triangles If ABC ≅ DEF & DEF ≅ JKL, Then ABC ≅ JKL B E K C F L A D J

12. Triangles XYZ ≅ MNL a. m<Y = ? b. YX = ? c. LMN ≅ ?
EX.
Triangles XYZ ≅ MNL
a. m<Y = ? b. YX = ? c. LMN ≅ ? L N X
124O 8
33O M Z Y

13. 4.3 Proving triangles congruent using SSS (side, side, side)

14. Side-side-side (sss) Congruent Postulate
If three sides of one triangle are congruent to three sides of a second triangle, Then the two triangles are congruent.
IF side AB ≅ DE, side BC ≅ EF, side AC ≅ DF,
THEN triangles ABC ≅ DEF B E A C D F

15. ex
Decide whether the congruence statement is true. Explain your reasoning. Z N Y X L M

16. ex
Decide whether the congruence statement is true. Explain your reasoning. B 3 7 A C 9 7 4 D

17. ex
Decide whether the congruence statement is true. Explain your reasoning. PQT ≅ RST P S Q T R

18. 4.4 Proving triangles congruent using SAS (side, ANGLE, side) & hl (Hypotenuse-Leg)

19. An angle in between two sides INCLUDED ANGLE

20. Side-ANGLE-side (sAs) Congruent Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, Then the two triangles are congruent.
IF side AB ≅ DE, angle <B ≅ <E, side BC ≅ EF,
THEN triangles ABC ≅ DEF B E A C D F

21. ex
Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate or theorem you would use. B C A D

22. ex
Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate or theorem you would use. D B C E A

23. ex
Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate or theorem you would use. B C D A F E

24. 4.5 Proving triangles congruent using ASA (ANGLE, SIDE, ANGLE) & AAS (ANGLE, ANGLE, SIDE)

25. ASA B E A C D F

26. D B C E A

27. AAS B E A C D F

28. D B C E A

29. Hypotenuse-Leg (HL) Congruent THEOREM
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, Then the two triangles are congruent.
IF side AB ≅ DE, side BC ≅ EF,
THEN triangles ABC ≅ DEF B E A C D F