unit 7: congruent triangles, and theorems final exam review

UNIT 7: CONGRUENT TRIANGLES, AND

THEOREMSFinal Exam Review

TOPICS TO INCLUDE

Corresponding Sides and AnglesCongruent TrianglesTriangle Sum TheoremMidsegment of a Triangle Theorem

CORRESPONDING SIDES AND ANGLESCongruent Triangles have: 3 congruent corresponding SIDES 3 congruent corresponding ANGLES

Use the CONGRUENT symbol (≅) to write out the congruent sides and anglesUse a LINE over the letters to write out the SIDESUse the angle symbol () to write out the angles

CORRESPONDING SIDES AND ANGLESExample

∆KJM ≅ ∆QPR ∠K ≅ ∠Q ∠J ≅ ∠P ∠M ≅ ∠R

CORRESPONDING SIDES AND ANGLESYou Try:

∆ANT ≅ ∆BUG

CONGRUENT TRIANGLES

There are 5 postulates that can prove that 2 triangles are congruentSSSSASASAAASHL

CONGRUENT TRIANGLES

SSS (Side Side Side)All 3 SIDES are congruent to each other

SAS (Side Angle Side)2 SIDES and the INCLUDED angle are congruent to each other

CONGRUENT TRIANGLES

ASA (Angle Side Angle)2 ANGLES and the INCLUDED side are congruent to each other

AAS (Angle Angle Side)2 ANGLES and the NON-INCLUDED side are congruent to each other

CONGRUENT TRIANGLES

HL (Hypotenuse leg)There must be a RIGHT angle2 sides must be marked

The HYPOTENUSE1 other LEG

CONGRUENT TRIANGLES

Determine how the triangles are congruent

1. 2. 3.

4. 5. 6.

TRIANGLE SUM THEOREM

The Triangle Sum Theorem states that the THREE angles in a triangle ALWAYS add up to 180°Example:

82 + 43 + X = 180

125 + X = 180

X = 55°

X

TRIANGLE SUM THEOREM

Now you try:

MIDSEGMENT OF A TRIANGLE THEOREMThe Midsegment of a Triangle Theorem states that the misdsegment of a triangle is equal to HALF of the THIRD sideBEFORE setting up an equation, MULTIPLY the midsegment by 2 and then solve.Example:

2(5X – 1) = 58

10X – 2 = 58

10X = 60

X = 6

MIDSEGMENT OF A TRIANGLE THEOREMNow you try:

ALL DONE