4.2 Apply Congruence and Triangles

4.2 Apply Congruence and Triangles

4.2 APPLY CONGRUENCE AND TRIANGLES What are congruent figures? Same size, same shape. In a figure, corresponding sides and corresponding angles are congruent. What are congruent figures? Same size, same shape. In a figure, corresponding sides and corresponding angles are congruent. Congruent

Ex. Not Congruent Congruence statements When you write a congruence statement for two polygons, always list the corresponding vertices in the same order. EX. E B A C

D F Congruence statements EX. B A E C

D ABC DEF F Congruence statements EX. E

B A C D Corresponding angles:

EX. E B A C D Corresponding sides: AB DE

BC EF AC DF F EX. ABCD EFGH Find x and y. B A C 102O

68O 84O 8 FT D (2y 4) FT E (2x-8) O F

H G Third ANGLES THEOREM triangle are congruent to two angles of another triangle, If two angles of one Then the third angles are also congruent. If

C D F EX. PTS RTQ Find

T 75 O Q R Properties of congruent triangles Property of Symmetric Congruent Triangles

Reflexive Property of Congruent Triangles For any triangle ABC, ABC ABC If ABC DEF, then DEF ABC B A K

E C D Transitive Property of Congruent Triangles If ABC DEF & DEF JKL, Then ABC JKL F J

L EX. a. m

33O M Y Z 4.3 Proving triangles congruent using SSS (side, side, side) Side-side-side (sss) Congruent Postulate triangle are congruent to three sides of a second triangle,

If three sides of oneThen the two triangles are congruent. IF side AB DE, side BC EF, side AC DF, THEN triangles ABC DEF E B A C D

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

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

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

4.4 Proving triangles congruent using SAS (side, ANGLE, side) & hl (Hypotenuse-Leg) Included angle An angle in between two sides INCLUDED ANGLE Side-ANGLE-side (sAs) Congruent Postulate

sides and the included angle of one triangle are congruent to two sides If two and the included angle of a second triangle, Then the two triangles are congruent. IF side AB DE, angle

D F 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

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 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 4.5 Proving triangles congruent using ASA (ANGLE, SIDE, ANGLE)

& AAS (ANGLE, ANGLE, SIDE) ASA E B A C D

F D B C E A AAS E B A

C D F D B C E A 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 E B A C

D F

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