Chapter 4: Q20WE. (page 157)

Given: $△ L M N ≅ △ R S T$ _; $\bar{L X}$ _{and $\bar{R Y}$ are altitudes.}
Prove: $\bar{L X} ≅ \bar{R Y}$

Short Answer

Expert verified

By corresponding parts of congruent triangles, it can be said that $\bar{L X} ≅ \bar{R Y}$ _.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

It is being given that $△ L M N ≅ △ R S T$ _.

Therefore, $L M ≅ R S$ , $∠ L M N ≅ ∠ R S T$ .

From the diagram, it can be seen that: $∠ L M N + ∠ L M X = 180 °$

and $∠ R S T + ∠ R S Y = 180 °$ .

Therefore, it can be obtained that:

$\begin{matrix} ∠ L M N + ∠ L M X = ∠ R S T + ∠ R S Y \\ ∠ L M N + ∠ L M X = ∠ L M N + ∠ R S Y \\ ∠ L M X = ∠ R S Y \end{matrix}$

Therefore, $∠ L M X ≅ ∠ R S Y$ .

Step 3. Description of step.

From the given diagram it can be noticed that $∠ L X M = ∠ R Y S = 90 °$ .

In the triangles $△ L M X$ and $△ R S Y$ , it can be noticed that $∠ L M X ≅ ∠ R S Y$ , $∠ L X M ≅ ∠ R Y S$ and $△ R S Y$ .

Therefore, the triangles $△ L M X$ and $△ R S Y$ are congruent triangles by using the AAS postulate.

Therefore, by corresponding parts of congruent triangles it can be said that $\bar{L X} ≅ \bar{R Y}$ _.

Hence proved.

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Given: $△ L M N ≅ △ R S T$ _; $\bar{L X}$ _{and $\bar{R Y}$ are altitudes.}
Prove: $\bar{L X} ≅ \bar{R Y}$

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Description of step.

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Given: △LMN≅△RST;LX¯and RY¯are altitudes.Prove:LX¯≅RY¯

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Geometry

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Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Given: $△ L M N ≅ △ R S T$ _; $\bar{L X}$ _{and $\bar{R Y}$ are altitudes.}
Prove: $\bar{L X} ≅ \bar{R Y}$