Triangle Theorems

Example: Isosceles Triangles

Example: Isosceles Triangles Name a pair of unmarked congruent segments. ___ BC is opposite D and BD is opposite BCD, so BC  BD. Answer: BC  BD

Example: Isosceles Triangles Which statement correctly names two congruent angles? A. PJM  PMJ B. JMK  JKM C. KJP  JKP D. PML  PLK A B C D

Example: Isosceles Triangles ALGEBRA Find the value of each variable. mDFE = 60 4x – 8 = 60 4x = 68 x = 17 DF = FE 6y + 3 = 8y – 5 3 = 2y – 5 8 = 2y 4 = y

Example: Isosceles Triangles Find the value of x and the measures of the unknown sides. X = 5 QS = RS = QR = 25 X = 11 LN = MN = 29

Name two congruent segments if 1  2. B. C. D. A B C D

Example: Exterior Angle Theorem Find the value of x and then find the measure of both angles. mLOW + mOWL = mFLW x + 32 = 2x – 48 32 = x – 48 80 = x Answer: So, mFLW = 2(80) – 48 or 112. and mF0W = 80

Example: Exterior Angle Theorem Find the measure of each missing angle m1 = 104 m2 = 76 m 3 = 42 m4 = 48 m5 = 49

Practice Find the measure of each missing angle

Angle-Side Relationship

Angle-Side Relationship You can list the angles and sides of a triangle from smallest to largest (or vice versa) The smallest side is opposite the smallest angle The longest side is opposite the largest angle

Angle-Side Relationship List the angles of ΔABC in order from smallest to largest. Answer: C, A, B

Angle-Side Relationship List the sides of ΔRST in order from shortest to longest. A. RS, RT, ST B. RT, RS, ST C. ST, RS, RT D. RS, ST, RT A B C D

EX: 1 x=15

EX: 2 x+x+15+3x=180 5x+15=180 5x=165 x=33

EX: 3 x-22+3x+19+x-17=180 5x-20=180 5x=200 x=40

EX: 4 x=138+21 x=159

EX: 5 42+x=77 x=35

EX: 6 x-6+x=148 2x-6=148 2x=154 x=77

EX: 7 x+4+x+3=127 2x+7=127 2x=120 x=60

EX: 8 Find the value of x <1=180-27-58=95° <3=180-132=48° <2=180-48-95=37° x=180-37=143°

EX: 9 <4=180-132-24=14° <2=180-93=87° <1=180-83-14=83°