UNIT 7: CONGRUENT TRIANGLES, AND THEOREMS Final Exam Review.

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Presentation transcript:

UNIT 7: CONGRUENT TRIANGLES, AND THEOREMS Final Exam Review

TOPICS TO INCLUDE  Corresponding Sides and Angles  Congruent Triangles  Triangle Sum Theorem  Midsegment of a Triangle Theorem

CORRESPONDING SIDES AND ANGLES

 You Try: ∆ANT ≅ ∆BUG

CONGRUENT TRIANGLES  There are 5 postulates that can prove that 2 triangles are congruent  SSS  SAS  ASA  AAS  HL

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 angle  2 sides must be marked  The HYPOTENUSE  1 other LEG

CONGRUENT TRIANGLES  Determine how the triangles are congruent

TRIANGLE SUM THEOREM  The Triangle Sum Theorem states that the THREE angles in a triangle ALWAYS add up to 180°  Example: X = X = 180 X = 55° X

TRIANGLE SUM THEOREM  Now you try:

MIDSEGMENT OF A TRIANGLE THEOREM  The Midsegment of a Triangle Theorem states that the misdsegment of a triangle is equal to HALF of the THIRD side  BEFORE 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 THEOREM  Now you try:

ALL DONE