Chapter 4: Q4. (page 136)

In the following figure, given the triangles at the right, which of the following can you conclude are true?
$\begin{array}{l} a . ∠ D ≅ ∠ R b . \bar{D E} ≅ \bar{D F} \\ c . \bar{D F} ≅ \bar{R T} d . ∠ E ≅ ∠ F \\ e . ∠ E ≅ ∠ S f . ∠ S ≅ ∠ T \end{array}$

Short Answer

Expert verified

The true statements are

$\begin{array}{l} b . \bar{D E} ≅ \bar{D F} \\ c . \bar{D F} ≅ \bar{R T} \\ d . ∠ E ≅ ∠ F \\ f . ∠ S ≅ ∠ T \end{array}$

Step by step solution

Step 1. Check the figure.

Consider the isosceles triangles.

Step 2. Apply the concept.

In an isosceles triangle, any two sides are always congruent. And angles opposite to these equal opposite sides are also congruent.

Step 3. Step description.

From the figures, it is clear that $\bar{D E} = \bar{R T} = 8$ .

Thus, $\bar{D E} ≅ \bar{R T}$ .

In $Δ D E F$ , as $\bar{D E} ≅ \bar{D F}$ so that $∠ E ≅ ∠ F$ .

Similarly, in $Δ R S T$ , as $\bar{R S} ≅ \bar{R T}$ so that $∠ S ≅ ∠ T$ .

Thus, the true statements are $\bar{D E} ≅ \bar{D F}, \bar{R S} ≅ \bar{R T}, ∠ E ≅ ∠ F$ and $∠ S ≅ ∠ T$ .

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In the following figure, given the triangles at the right, which of the following can you conclude are true?
$\begin{array}{l} a . ∠ D ≅ ∠ R b . \bar{D E} ≅ \bar{D F} \\ c . \bar{D F} ≅ \bar{R T} d . ∠ E ≅ ∠ F \\ e . ∠ E ≅ ∠ S f . ∠ S ≅ ∠ T \end{array}$

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept.

Step 3. Step description.

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In the following figure, given the triangles at the right, which of the following can you conclude are true?a.∠D≅∠Rb.DE¯≅DF¯c.DF¯≅RT¯d.∠E≅∠Fe.∠E≅∠Sf.∠S≅∠T

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

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Geometry

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Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following figure, given the triangles at the right, which of the following can you conclude are true?
$\begin{array}{l} a . ∠ D ≅ ∠ R b . \bar{D E} ≅ \bar{D F} \\ c . \bar{D F} ≅ \bar{R T} d . ∠ E ≅ ∠ F \\ e . ∠ E ≅ ∠ S f . ∠ S ≅ ∠ T \end{array}$