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Chapter 3: Q24 (page 82)

Given: AS¯∥BT¯;m∠4=m∠5

Prove SA→bisects ∠BSR

Short Answer

Expert verified

Since, line segments SB¯andRT¯are transversal to parallel lines

∠1and ∠4forms a pair of corresponding angles

m∠1=m∠41

role="math" localid="1637817679668" ∠2and ∠5forms a pair of alternate interior angles

m∠2=m∠52

Substitute m∠1form∠4 and m∠2for m∠5in given equation

m∠4=m∠5m∠1=m∠2

Thus, SA→bisects ∠BSR

Step by step solution

01

Step 1. Observe from figure

Line segments SB¯andRT¯are transversal to parallel lines

02

Step 2. Corresponding angles

∠1and ∠4forms a pair of corresponding angles

Using Postulate 10: If two parallel lines are cut by transversal, then corresponding angles are congruent.

∠1≅∠4

m∠1=m∠41

03

Step 3. Alternate interior angles

∠2and ∠5forms a pair of alternate interior angles

Using theorem 3-2: If two parallel lines are cut by transversal, then alternate interior angles are congruent.

∠2≅∠5

m∠2=m∠52

04

Step 4. Use given statement with equations (1) and (2)

Substitute m∠1form∠4 and m∠2for m∠5in given equation

m∠1=m∠2

Thus, SA→bisects ∠BSR

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Most popular questions from this chapter

Classify each pair of angles as alternate interior, same side interior or corresponding angles

art

and

Name the two lines and the transversal that form each pair of angles.

and

Find the values of xand y

If a∥b, name all angels that must be congruent to ∠1.

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

.Name two planes parallel toAB¯.
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