47. Coordinate Geometry In Δ G H J , K ( 2 , 3 ) cap delta g h j comma k open 2 comma 3 close  is the midpoint of G H ¯ , g h bar , comma  L(4, 1) is the midpoint of H J ¯ , h j bar , comma  and M(6, 2) is the midpoint of G J ¯ . g j bar , .  Find the coordinates of G, H, and J.

48. Proof Complete the Prove statement and then write a proof.

    Given: In Δ V Y Z , S , T , cap delta v y z comma s comma t comma  and U are midpoints.

    Prove: Δ Y S T ≅ Δ T U Z ≅ Δ S V U ≅ ? ¯ cap delta y s t approximately equal to cap delta t u z approximately equal to cap delta s v u approximately equal to , modified question mark with under bar below

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

Use the figure below for Exercises 49 and 50. Your home is at point H. Your friend lives at point F, the midpoint of Elm Street. Elm Street intersects Beech Street and Maple Street at their midpoints.

Image Long Description

49. Your friend walks to school by going east on Elm and then turning right on Maple. How far in miles does she walk?
50. You walk your dog along this route: Walk from home to Elm along Maple. Walk west on Elm to Beech, south on Beech to the library, and east on Oak to school. Then walk back home along Maple. How far in miles do you walk?

For Exercises 51 and 52, Δ A B C cap delta eh b c  is a triangle in which m ∠ A = 30 bold italic m angle eh equals 30  and ∠ B = 70 . angle b , equals 70 .   P, Q, and R are the midpoints of A B ¯ , B C ¯ , eh b bar , comma . b c bar , comma  and C A ¯ , c eh bar , comma  respectively.

51. What is the measure, in degrees, of ∠ R P Q ? angle r p q question mark
52. If Q P = 2 x + 17 q p equals . 2 x plus 17  and C A = x + 97 , c eh equals . x plus 97 , comma  what is CA?

Mixed Review

See Problem 4-7.

Use the figure below for Exercises 53 and 54.

53. List all the pairs of congruent triangles that you can find in the figure.
54. Given: F D ¯ ≅ F E ¯ , B F ¯ ≅ C F ¯ , ∠ 1 ≅ ∠ 2 f d bar , approximately equal to . f e bar , comma . b f bar , approximately equal to . c f bar , comma . angle 1 approximately equal to angle 2

    Prove: A B ¯ ≅ A C ¯ eh b bar , approximately equal to , eh c bar

Get Ready! To prepare for Lesson 5-2, do Exercises 55–57.

See Problem 1-5.

T M ¯ t m bar  bisects ∠ S T U angle s t u  so that m ∠ S T M = 5 x + 4 bold italic m angle s t m equals 5 bold italic x plus 4  and m ∠ M T U = 6 x − 2 . bold italic m angle m t u equals 6 bold italic x minus 2 .

55. Find the value of x.
56. Find m ∠ S T U . m angle s t u .

See Lesson 1-6.

57. Draw acute ∠ E . angle e .  Construct the bisector of ∠ E . angle e .

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