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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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