Chapter 4: Q9. WE (page 137)

For each exercise place the statements in an appropriate order for a proof. (There may be more than one correct order.)
Given: $\bar{RS} ≅ \bar{RT}$
Prove: $∠ 3 ≅ ∠ 4$
(a) $∠ 3 ≅ ∠ 4$
(b) $∠ 3 ≅ ∠ 1; ∠ 2 ≅ ∠ 4$
(c) $\bar{RS} ≅ \bar{RT}$
(d) $∠ 1 ≅ ∠ 2$

Short Answer

Expert verified

Order of the proof is $(c), (d), (b) and (a)$ .

Step by step solution

Step 1. Apply isosceles triangle theorem.

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

From the figure it can be observed that, $\bar{R S} ≅ \bar{R T}$ .

Therefore, $∠ 1 ≅ ∠ 2$ .

Step 2. Vertically opposite angles.

From the figure it can be observed that, $∠ 1 and ∠ 3$ , $∠ 2 and ∠ 4$ are vertically opposite angles. Therefore,

$\begin{matrix} ∠ 1 ≅ ∠ 3 \\ ∠ 2 ≅ ∠ 4 \end{matrix}$

Step 3. Transitive property of congruence.

If $∠ P ≅ ∠ Q$ and $∠ Q ≅ ∠ S$ then $∠ P ≅ ∠ S$ .

Therefore, $∠ 3 ≅ ∠ 4$ .

From the above explanation, the order of proof is $(c), (d), (b) and (a)$ .

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For each exercise place the statements in an appropriate order for a proof. (There may be more than one correct order.)
Given: $\bar{RS} ≅ \bar{RT}$
Prove: $∠ 3 ≅ ∠ 4$
(a) $∠ 3 ≅ ∠ 4$
(b) $∠ 3 ≅ ∠ 1; ∠ 2 ≅ ∠ 4$
(c) $\bar{RS} ≅ \bar{RT}$
(d) $∠ 1 ≅ ∠ 2$

Short Answer

Step by step solution

Step 1. Apply isosceles triangle theorem.

Step 2. Vertically opposite angles.

Step 3. Transitive property of congruence.

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For each exercise place the statements in an appropriate order for a proof. (There may be more than one correct order.)Given:RS¯≅RT¯Prove:∠3≅∠4(a)∠3≅∠4(b)∠3≅∠1;∠2≅∠4(c)RS¯≅RT¯(d)∠1≅∠2

Short Answer

Step by step solution

Step 1. Apply isosceles triangle theorem.

Step 2. Vertically opposite angles.

Step 3. Transitive property of congruence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Geometry

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For each exercise place the statements in an appropriate order for a proof. (There may be more than one correct order.)
Given: $\bar{RS} ≅ \bar{RT}$
Prove: $∠ 3 ≅ ∠ 4$
(a) $∠ 3 ≅ ∠ 4$
(b) $∠ 3 ≅ ∠ 1; ∠ 2 ≅ ∠ 4$
(c) $\bar{RS} ≅ \bar{RT}$
(d) $∠ 1 ≅ ∠ 2$