Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Complete each statement. Explain why it is true.

6. V T ¯ ≅ v t bar , approximately equal to  __?__
7. U T ¯ ≅ u t bar , approximately equal to  __?__ ≅ Y X ¯ approximately equal to , y x bar
8. V U ¯ ≅ v u bar , approximately equal to  __?__
9. ∠ V Y U ≅ angle v y u approximately equal to  __?__

See Problem 2.

Algebra Find the values of x and y.

10. 
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11. 
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12. 

See Problem 3.

13. An equilateral triangle and an isosceles triangle share a common side. What is the measure of ∠ A B C ? angle eh b c question mark

B Apply

14. Architecture Each face of the Great Pyramid at Giza is an isosceles triangle with a 76 ° 76 degrees  vertex angle. What are the measures of the base angles?
15. Reasoning What are the measures of the base angles of a right isosceles triangle? Explain.

Given isosceles Δ J K L cap delta j k l  with base J L ¯ j l bar  find each value.

16. If m ∠ L = 58 , m angle . l equals 58 comma  then m ∠ L K J = m angle l k j . equals  __?__.
17. If J L = 5 , j l equals 5 comma  then M L = m l equals  __?__.
18. If m ∠ J K M = 48 , m angle j k m . equals 48 comma  then m ∠ J = m angle , j equals  __?__.

19. If m ∠ J = 55 , m angle . j equals 55 comma  then m ∠ J K M = m angle j k m . equals  __?__.

    

20. Think About a Plan A triangle has angle measures x + 15 , 3 x − 35 , x plus 15 comma . 3 x minus 35 comma  and 4x. What type of triangle is it? Be as specific as possible. Justify your answer.
    • What do you know about the sum of the angle measures of a triangle?
    • What do you need to know to classify a triangle?
    • What type of triangle has no congruent angles? Two congruent angles? Three congruent angles?
21. Reasoning An exterior angle of an isosceles triangle has measure 100. Find two possible sets of measures for the angles of the triangle.

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