Q4. Complete.If聽RK炉聽is both an al... [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: Q4. (page 155)

Complete.
If $\overset{炉}{R K}$ is both an altitude and a median of $螖 R S T$ , then:
$螖 R S K 鈮� 螖 R T K$ by $\underset{炉}{?}$
$螖 R S T$ is $a (n) \underset{炉}{?}$ triangle

Short Answer

Expert verified

a. $螖 R S K 鈮� 螖 R T K$ by SAS Postulate.

b. $螖 R S T$ is an isosceles triangle

Step by step solution

Part a. Step 1. Definition of median and altitude.

The altitude is perpendicular line segment from vertex to opposite side of thetriangle.

The median is a line segment from vertex to midpoint of the opposite side of the triangle.

Part a. Step 2. Show that ΔRSK≅ΔRTK

Statement	Reason
1. $\overset{炉}{R K} 鈮� \overset{炉}{R K}$	Common line segment
2. $鈭� R K S 鈮� 鈭� R K T$	Altitude divides adjacent angles into congruent angles
3. $\overset{炉}{S K} 鈮� \overset{炉}{T K}$	$K$ is midpoint of $\overset{炉}{S T}$ , so divide it into two congruent sides
4. $螖 R S K 鈮� 螖 R T K$	SAS (Side-Angle-Side)Postulate

Part a. Step 3. Complete the given statement.

$螖 R S K 鈮� 螖 R T K$ by SAS Postulate.

Part b. Step 1. Definition of Isosceles triangle.

A triangle is isosceles when two of its sides are congruent

Part b. Step 2. Show that SR¯≅TR¯

Statement	Reason
1. $\overset{炉}{R K} 鈮� \overset{炉}{R K}$	Common line segment
2. $鈭� R K S 鈮� 鈭� R K T$	Altitude divides adjacent angles into congruent angles
3. $\overset{炉}{S K} 鈮� \overset{炉}{T K}$	$K$ is midpoint of $\overset{炉}{S T}$ , so divide it into two congruent sides
4. $螖 R S K 鈮� 螖 R T K$	SAS (Side-Angle-Side)Postulate
5. $\overset{炉}{S R} 鈮� \overset{炉}{T R}$	Corresponding parts of congruent triangle

Part b. Step 3. Complete the given statement.

$螖 R S T$ is an isosceles triangle

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91影视

Complete.
If $\overset{炉}{R K}$ is both an altitude and a median of $螖 R S T$ , then:
$螖 R S K 鈮� 螖 R T K$ by $\underset{炉}{?}$
$螖 R S T$ is $a (n) \underset{炉}{?}$ triangle

Short Answer

Step by step solution

Part a. Step 1. Definition of median and altitude.

Part a. Step 2. Show that ΔRSK≅ΔRTK

Part a. Step 3. Complete the given statement.

Part b. Step 1. Definition of Isosceles triangle.

Part b. Step 2. Show that SR¯≅TR¯

Part b. Step 3. Complete the given statement.

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91影视

Complete.IfRK炉is both an altitude and a median of 螖RST, then:螖RSK鈮�螖RTKby ?炉螖RSTis a(n)?炉triangle

Short Answer

Step by step solution

Part a. Step 1. Definition of median and altitude.

Part a. Step 2. Show that ΔRSK≅ΔRTK

Part a. Step 3. Complete the given statement.

Part b. Step 1. Definition of Isosceles triangle.

Part b. Step 2. Show that SR¯≅TR¯

Part b. Step 3. Complete the given statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Complete.
If $\overset{炉}{R K}$ is both an altitude and a median of $螖 R S T$ , then:
$螖 R S K 鈮� 螖 R T K$ by $\underset{炉}{?}$
$螖 R S T$ is $a (n) \underset{炉}{?}$ triangle