1. Properties of Equality- A ddition Property: If a=b, then a+c=b+c Subtraction Property: If a=b, then a-c=b-c Multiplication Property: If a=b, then a*c=b*c Division Property: If a=b and c≠0, then a/c=b/c Reflexive Property: a=a Symmetric Property: If a=b, then b=a Transitive Property: If a=b and b=c, then a=c Substitution Property: If a=b, then b can replace a in any expression D istributive Property: a(b+c)=ab+ac Properties of Congruence- R eflexive Property: AB ≅ AB <A ≅ <A Symmetric Property: If AB ≅ CD, then CD ≅ AB If <A ≅ <B, then <B ≅ <A Transitive Property: If AB ≅ CD and CD ≅ EF, then AB ≅ EF If <A ≅ <B and <B ≅ <C, then <A ≅ <C

2. Use the given property to complete each statement. 1. Symmetric Property of Equality If MN=UT, then ___UT=MN__________? 2. Division Property of Equality If 4m<QWR=120, then ___m<QWR=30________? 3. Transitive Property of Equality If SB=VT and VT=MN, then ___SB=MN________? 4. Addition Property of Equality If y-15=36, then ____y=51________? 5. Reflexive Property of Congruence JL ≅ _JL___? Name the property that justifies each statement 1. If m<G=35 and m<S=35, then m<G ≅ m<S 2. If 10x+6y=14 and x=2y, then 10(2y)+6y=14 3.If TR=MN and MN=VW, then TR=VW 4. If JK ≅ LM, then LM ≅ JK 5. If <Q ≅ <S and <S ≅ <P, then <Q ≅ <P Move the boxes to check your answers! *Substitution Property *Transitive Property *Symmetric Property *Transitive Property

3. Everything Triangles!! classification:

4. Investigation: How Many Degrees are in a Triangle?? How many Degrees are in a Quadrilateral? Pentagon? Hexagon? etc...? Polygon# of sides# of triangles formed Sum of the interior angle measures Polygon Angle-Sum Theorem- The sum of the measures of the angles of an n-gon is (n-2)*180 Triangle Angle-Sum Theorem: T he sum of the measures of the angles of a triangle is 180.

5. Triangle Exterior Angle Theorem: T he measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. 52.2 44.7 x 11 3 x 70 33 11 7 x x y z 40 30 80 y x 70 30 Exterior Angle- angle formed by a side and an extension of an adjacent side. Remote Interior Angles- The two nonadjacent interior angles 33+117=150 180-150= 30 52.2+44.7=96.9 180-96.9= 83.1 113-70=43 80+30=110 x=180-110=70 y=180-70=110 z=180-(110+40)=30 70+30=100 x=180-100=80 y=80 x&y are vertical angles

6. More Practice!! F ind the values of x,y, and z. 1. 39 21 z y x 65 Find the values of the variables 2. 55 c d 32 b a e x=76 y=104 z=55 a=67 b=58 c=125 d=23 e=90

7. Isosceles Triangles: The congruent sides of an isosceles triangle are its legs. The third side is the base. The two congruent sides form the vertex angle. The other two angles are the base angles. Isosceles Triangle Theorem- If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of Isosceles Triangle Theorem- If two angles of a triangle are congruent, then the sides opposite the angles are congruent. Corollary- If a triangle is equilateral, then the triangle is equiangular. If a triangle is equiangular, then the triangle is equilateral. Practice: Isos. Triangles 55 x 1. 2. 66 x x=31.25 x=42

8. A midsegment is a segment connecting the midpoint of each side. Triangle Midsegment Theorem: The midsegment is parallel to the third side, and is half its length. Examples: 1) x 20 2) 3 3 4 4 x-1 5 3) 5x 70 x=10 x=11 x=7