Q10. The two triangles shown are cong... [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: Q10. (page 120)

The two triangles shown are congruent. Complete.
a. $螖 S T O 鈮�$ ? .
b. $鈭� S 鈮�$ ? because ?.
c. $鈭� S O 鈮�$ ? because ? .
Then point O is the midpoint of? .
d. $鈭� T 鈮�$ ? because ?.
Then $\overset{炉}{S T} 鈭� \overset{炉}{R K}$ because ?.

Short Answer

Expert verified

a. $螖 S T O 鈮� \underset{炉}{螖 K R O}$

b. $鈭� S 鈮� \underset{炉}{鈭� K}$ because when two triangles are congruent, then its corresponding parts are also congruent.

c. $\overset{炉}{S O} 鈮� \underset{炉}{\overset{炉}{O K}}$ because when two triangles are congruent, then its corresponding parts are also congruent.

Then $O$ is the midpoint of $\underset{炉}{\overset{炉}{S K}}$ .

d. $鈭� T 鈮� \underset{炉}{鈭� R}$ because when two triangles are congruent, then its corresponding parts are also congruent.

Then $\overset{炉}{S T} 鈭� \overset{炉}{R K}$ because alternate interior angles cut by a transversal are equal, that is, $\underset{炉}{鈭� S 鈮� 鈭� K}$ and $\underset{炉}{鈭� T 鈮� 鈭� R}$ .

Step by step solution

Part a. Step 1. Consider the diagram.

Here, the two triangles are congruent.

Part a. Step 2. State the explanation.

As, the triangles are congruent, $螖 S T O$ is congruent to $螖 K R O$ .

Part a. Step 3. State the conclusion.

Therefore, $螖 S T O 鈮� 螖 K R O$ .

Part b. Step 1. Consider the diagram.

Here, the two triangles are congruent.

Part b. Step 2. State the explanation.

As $螖 S T O 鈮� 螖 K R O$ , its corresponding parts are also congruent.

Part b. Step 3. State the conclusion.

Therefore, $鈭� S 鈮� 鈭� K$ .

Part c. Step 1. Consider the diagram.

Here, the two triangles are congruent.

Part c. Step 2. State the explanation.

As $螖 S T O 鈮� 螖 K R O$ , its corresponding parts are also congruent.

Part c. Step 3. State the conclusion.

Therefore, $\overset{炉}{S O} 鈮� \overset{炉}{O K}$ and as $\overset{炉}{S O} = \overset{炉}{O K}$ , O is the midpoint of $\overset{炉}{S K}$ since midpoint divides a line segment into two equal parts.

Part d. Step 1. Consider the diagram.

Here, the two triangles are congruent.

Part d. Step 2. State the explanation.

As $螖 S T O 鈮� 螖 K R O$ , its corresponding parts are also congruent.

Part d. Step 3. State the conclusion.

Therefore, $鈭� T 鈮� 鈭� R$ .

$\overset{炉}{S T}$ is parallel to $\overset{炉}{R K}$ because alternate interior angles cut by a transversal are equal, that is, $鈭� S 鈮� 鈭� K$ and $鈭� T 鈮� 鈭� R$ .

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91影视

The two triangles shown are congruent. Complete.
a. $螖 S T O 鈮�$ ? .
b. $鈭� S 鈮�$ ? because ?.
c. $鈭� S O 鈮�$ ? because ? .
Then point O is the midpoint of? .
d. $鈭� T 鈮�$ ? because ?.
Then $\overset{炉}{S T} 鈭� \overset{炉}{R K}$ because ?.

Short Answer

Step by step solution

Part a. Step 1. Consider the diagram.

Part a. Step 2. State the explanation.

Part a. Step 3. State the conclusion.

Part b. Step 1. Consider the diagram.

Part b. Step 2. State the explanation.

Part b. Step 3. State the conclusion.

Part c. Step 1. Consider the diagram.

Part c. Step 2. State the explanation.

Part c. Step 3. State the conclusion.

Part d. Step 1. Consider the diagram.

Part d. Step 2. State the explanation.

Part d. Step 3. State the conclusion.

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91影视

The two triangles shown are congruent. Complete.a. 螖STO鈮�? .b. 鈭�S鈮�? because ?.c. 鈭�SO鈮�? because ? .Then point O is the midpoint of? .d. 鈭�T鈮�? because ?.Then ST炉鈭�RK炉because ?.

Short Answer

Step by step solution

Part a. Step 1. Consider the diagram.

Part a. Step 2. State the explanation.

Part a. Step 3. State the conclusion.

Part b. Step 1. Consider the diagram.

Part b. Step 2. State the explanation.

Part b. Step 3. State the conclusion.

Part c. Step 1. Consider the diagram.

Part c. Step 2. State the explanation.

Part c. Step 3. State the conclusion.

Part d. Step 1. Consider the diagram.

Part d. Step 2. State the explanation.

Part d. Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Calculus

Applied Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

The two triangles shown are congruent. Complete.
a. $螖 S T O 鈮�$ ? .
b. $鈭� S 鈮�$ ? because ?.
c. $鈭� S O 鈮�$ ? because ? .
Then point O is the midpoint of? .
d. $鈭� T 鈮�$ ? because ?.
Then $\overset{炉}{S T} 鈭� \overset{炉}{R K}$ because ?.