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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