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Chapter 3: Q32 (page 99)

Given: PRbisects 鈭�SPQand PS鈯�SQ;RQ鈯�PQ.

Which numbered angles must be congruent?

Short Answer

Expert verified

The congruent angles are 鈭�7鈮�鈭�8and 鈭�11鈮�鈭�12.

Step by step solution

01

Step 1. Apply the definition of angle bisector.

Angle bisector is a line which divides an angle into two equal parts.

From the figure, it can be observed that PR炉bisect 鈭�SPQ. Therefore,

鈭�7鈮�鈭�8

02

Step 2. Description of step.

PS炉鈯�SQ炉and RQ炉鈯�PQ炉, therefore,

鈭�Q鈮�鈭�Sm鈭�Q=90

03

Step 3. Description of step.

Consider 螖PQRand螖PST, in which 鈭�Q鈮�鈭�S,鈭�RPQ鈮�鈭�SPTimplies that 鈭�PTS鈮�鈭�11.

04

Step 4. Apply definition of vertically opposite angles.

Vertically opposite angles are the opposite angles formed due to intersection of two lines.

Consider 螖PQRand螖PST,

鈭�11and鈭�12are vertically opposite angles, therefore, 鈭�11鈮�鈭�12.

Therefore, the congruent angles are 鈭�7鈮�鈭�8and 鈭�11鈮�鈭�12.

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Most popular questions from this chapter

  1. Draw two parallel lines and a transversal.
  2. Use a protractor to draw bisectors of two same-side interior angles.
  3. Measure the angles formed by the bisectors. What do you notice?
  4. Prove your answer to part (c).

If c鈭�d, name all angels that must be congruent to 鈭�1.

Complete each statement with the word always, sometimes, or never.

A line in the plane of a wall and a line in the plane of the floor are

a. _?_Parallel.

b. _?_intersecting.

c. _?_skew.

The sum of the measures of the interior angles of a polygon is known to be between 2100 and 2200. How many sides does the polygon have?

If ED炉AC炉and EB炉DC炉, name all pairs of angles that must be congruent.
See all solutions

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