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Today you will Use properties of isosceles triangles and equilateral triangles to find missing dimensions of triangles. Use CPCTC to prove corresponding parts of triangles are = 4.6 Isosceles Triangles and Equilateral Triangles base angle leg base base angle vertex angle vertex leg Isosceles Triangle Theorem: If 2 sides of a triangle are those sides are . , then the angles opposite Converse of the Isosceles Triangle Theorem: If two angles of a triangle are those angles are . , then the sides opposite 2. Find m G 1. Find m F. E G 22o D x+44o F J 3xo H Corollaries for Equilateral Triangles A triangle is equilateral IFF it is equiangular. ) then | | 2. ) Example: If ) 1. | o Each angle of an equilateral triangle measures 60 2x+32o ( Find x. Find y. 5y-6 4y+12 B Given: Prove: ABC is isosceles EB bisects ABC ABE A CBE Statement 1. ABC is isosceles EB bisects ABC E Reason 1. CPCTC: Corresponding Parts of Congruent Triangles are Congruent B Given: Prove: ABC is isosceles EB bisects ABC AE Statement CE A E C Reason Q S R P Given: P PX RX X T T Y Prove: TY RY Statement 1. PX Reason 1. T P TY 2. PX = TY 2. 3. XY = YX 3. 4. PX + XY = PY and TY + YX =TX 4. 5. PY = TX 5. 6. PY 6. 7. RX TX 7. RY 8. 8. 9. 10. Q PQY TSX 9. 10. S Given: MS TR MS = TR Prove: MA M R A TA S Statement T Reason