Isosceles and Equilateral Triangles CONCEPT 25 1 Has

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Isosceles and Equilateral Triangles CONCEPT 25 1

Isosceles and Equilateral Triangles CONCEPT 25 1

Has exactly three congruent sides Vertex Angle Leg the angle formed by the legs.

Has exactly three congruent sides Vertex Angle Leg the angle formed by the legs. the 2 congruent sides of an isosceles triangle. Base Angle 2 angles adjacent to the base. Base the 3 rd side of an isosceles triangle 2

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1. Name two unmarked congruent angles. ___ BCA is opposite BA and ___ A

1. Name two unmarked congruent angles. ___ BCA is opposite BA and ___ A is opposite BC, so BCA A. Answer: BCA and A 4

2. Name two unmarked congruent segments. ___ BC is opposite D and ___ BD

2. Name two unmarked congruent segments. ___ BC is opposite D and ___ BD is opposite BCD, so ___ BC BD. Answer: BC BD 5

3. Which statement correctly names two congruent angles? A. PJM PMJ B. JMK JKM

3. Which statement correctly names two congruent angles? A. PJM PMJ B. JMK JKM C. KJP JKP D. PML PLK 6

4. Which statement correctly names two congruent segments? A. JP PL B. PM PJ

4. Which statement correctly names two congruent segments? A. JP PL B. PM PJ C. JK MK D. PM PK 7

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5. Find m R. Since QP = QR, QP QR. By the Isosceles Triangle

5. Find m R. Since QP = QR, QP QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so m P = m R. Use the Triangle Sum Theorem to write and solve an equation to find m R. Triangle Sum Theorem m Q = 60, m P = m R Answer: m R = 60 Simplify. Subtract 60 from each side. Divide each side by 2. 9

6. Find PR. Since all three angles measure 60, the triangle is equiangular. Because

6. Find PR. Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution. Answer: PR = 5 cm 10

A. Find m T. A. 30° B. 45° C. 60° D. 65° 11

A. Find m T. A. 30° B. 45° C. 60° D. 65° 11

B. Find TS. A. 1. 5 B. 3. 5 C. 4 D. 7 12

B. Find TS. A. 1. 5 B. 3. 5 C. 4 D. 7 12

7. Find the value of each variable. m DFE = 60 4 x –

7. Find the value of each variable. m DFE = 60 4 x – 8 = 60 4 x = 68 x = 17 The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal. DF = FE 6 y + 3 = 8 y – 5 3 = 2 y – 5 8 = 2 y 4 =y 13

8. Find the value of each variable. A. x = 20, y = 8

8. Find the value of each variable. A. x = 20, y = 8 B. x = 20, y = 7 C. x = 30, y = 8 D. x = 30, y = 7 14

C T C P C C O N C E P T 2 6

C T C P C C O N C E P T 2 6 15

Corresponding Parts of Congruent Triangles are Congruent 16

Corresponding Parts of Congruent Triangles are Congruent 16

Use the diagram to answer the following. • What triangle appears to be congruent

Use the diagram to answer the following. • What triangle appears to be congruent to PAS? • What triangle appears to be congruent to PAR? 17

Use the diagram to answer the following questions. LPS APS LRS ARS LPS ARS

Use the diagram to answer the following questions. LPS APS LRS ARS LPS ARS APS LRS 18

Use the marked diagrams to state the method used to prove the triangles are

Use the marked diagrams to state the method used to prove the triangles are congruent. Give the congruence statement, then name the additional corresponding parts that could then be concluded to be congruent. Missing Info/Why: Symmetric Prop. Triangle Congruence/Why: SSS CPCTC: 19

Use the marked diagrams to state the method used to prove the triangles are

Use the marked diagrams to state the method used to prove the triangles are congruent. Give the congruence statement, then name the additional corresponding parts that could then be concluded to be congruent. Missing Info/Why: Vertical Angles Triangle Congruence/Why: ASA CPCTC: 20

 Statements 1. Given 2. S R 3. 5. Reasons 2. Given 3. Vertical

Statements 1. Given 2. S R 3. 5. Reasons 2. Given 3. Vertical Angles 4. ASA 5. CPCTC 21