5 Mid-Chapter Quiz

Do you know HOW?

Algebra Find the value of x.

Use the figure below for Exercises 3–5.

3. Find YZ.
4. A X = 26 eh x equals 26  and B Z = 36 . b z equals 36 . .  Find the perimeter of Δ X Y Z . cap delta x y z .
5. Which angle is congruent to ∠ X B A ? angle x b eh question mark  How do you know?

For the figure below, what can you conclude about each of the following? Explain.

6. ∠ C D B angle c d b
7. Δ A B D cap delta eh b d  and Δ C B D cap delta c b d
8. A D ¯ eh d bar  and D C ¯ d c bar

In the figure below, P is the centroid of Δ A B C . cap delta eh b c .

9. If P R = 6 , p r equals 6 , comma  find AP and AR.
10. If P B = 6 , p b equals 6 , comma  find QP and QB.
11. If S C = 6 , s c equals 6 , comma  find CP and PS.

For Δ A B C , cap delta eh b c comma  is the red line a perpendicular bisector, an angle bisector, a median, an altitude, or none of these? Explain.

12. 
13. 
14. 
15. Δ P Q R cap delta p q r  has vertices P(2, 5), Q(8, 5), and R(8, 1). Find the coordinates of the circumcenter and the orthocenter of Δ P Q R . cap delta p q r .

Do you UNDERSTAND?

16. Writing Explain how to construct a median of a triangle and an altitude of a triangle.
17. Error Analysis Point O is the incenter of scalene Δ X Y Z . cap delta x y z .  Your friend says that m ∠ Y X O = m ∠ Y Z O . m angle y x o equals m angle y z o .  Is your friend correct? Explain.

The sides of Δ D E F cap delta d e f  are the midsegments of Δ A B C . cap delta eh b c .

The sides of Δ G H I cap delta g h i  are the midsegments of Δ D E F . cap delta d e f .

18. Which sides, if any, of Δ G H I cap delta g h i  and Δ A B C cap delta eh b c  are parallel? Explain.
19. What are the relationships between the side lengths of Δ G H I cap delta g h i  and Δ A B C ? cap delta eh b c question mark  Explain.

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