Q21. Given:聽OP炉鈮匫Q炉;鈭�3鈮呪垹4P... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q21. (page 138)

Given: $\overset{炉}{OP} 鈮� \overset{炉}{OQ}; 鈭� 3 鈮� 鈭� 4$
Prove: $鈭� 5 鈮� 鈭� 6$

Short Answer

Expert verified

It is proved that $鈭� 5 鈮� 鈭� 6$ .

Step by step solution

Step 1. Vertically opposite angles.

From the figure it can be observed that, $鈭� P O S$ and $鈭� Q O R$ are vertically opposite angles. Therefore, $鈭� P O S 鈮� 鈭� Q O R$ .

Step 2. ASA postulate.

If two angles and included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Here, $鈭� 3 鈮� 鈭� 4$ , $\overset{炉}{O P} 鈮� \overset{炉}{O Q}$ and $鈭� P O S 鈮� 鈭� Q O R$ , then by ASA postulate width="112" height="20" role="math">螖POS鈮�螖QOR.

Step 3. Description of step.

As $螖 P O S 鈮� 螖 Q O R$ , implies that sides of congruent angles are congruent, that is, $\overset{炉}{O S} 鈮� \overset{炉}{O R}$ .

Step 4. Isosceles triangle theorem.

If two sides of triangle are congruent then the angles opposite to those sides are congruent.

Consider $螖 O S R,$ as $\overset{炉}{O S} 鈮� \overset{炉}{O R}$ , therefore, by isosceles triangle theorem, $鈭� 5 鈮� 鈭� 6$ .

Hence it is proved that, $鈭� 5 鈮� 鈭� 6$ .

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91影视

Given: $\overset{炉}{OP} 鈮� \overset{炉}{OQ}; 鈭� 3 鈮� 鈭� 4$
Prove: $鈭� 5 鈮� 鈭� 6$

Short Answer

Step by step solution

Step 1. Vertically opposite angles.

Step 2. ASA postulate.

Step 3. Description of step.

Step 4. Isosceles triangle theorem.

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91影视

Given:OP炉鈮�OQ炉;鈭�3鈮�鈭�4Prove:鈭�5鈮�鈭�6

Short Answer

Step by step solution

Step 1. Vertically opposite angles.

Step 2. ASA postulate.

Step 3. Description of step.

Step 4. Isosceles triangle theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Probability and Statistics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Given: $\overset{炉}{OP} 鈮� \overset{炉}{OQ}; 鈭� 3 鈮� 鈭� 4$
Prove: $鈭� 5 鈮� 鈭� 6$