Chapter 4: Q4. (page 155)

Complete.
If $\bar{R K}$ is both an altitude and a median of $Δ R S T$ , then:
$Δ R S K ≅ Δ R T K$ by $\underline{?}$
$Δ R S T$ is $a (n) \underline{?}$ triangle

Short Answer

Expert verified

a. $Δ R S K ≅ Δ R T K$ by SAS Postulate.

b. $Δ R S T$ 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. $\bar{R K} ≅ \bar{R K}$	Common line segment
2. $∠ R K S ≅ ∠ R K T$	Altitude divides adjacent angles into congruent angles
3. $\bar{S K} ≅ \bar{T K}$	$K$ is midpoint of $\bar{S T}$ , so divide it into two congruent sides
4. $Δ R S K ≅ Δ R T K$	SAS (Side-Angle-Side)Postulate

Part a. Step 3. Complete the given statement.

$Δ R S K ≅ Δ R T K$ 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. $\bar{R K} ≅ \bar{R K}$	Common line segment
2. $∠ R K S ≅ ∠ R K T$	Altitude divides adjacent angles into congruent angles
3. $\bar{S K} ≅ \bar{T K}$	$K$ is midpoint of $\bar{S T}$ , so divide it into two congruent sides
4. $Δ R S K ≅ Δ R T K$	SAS (Side-Angle-Side)Postulate
5. $\bar{S R} ≅ \bar{T R}$	Corresponding parts of congruent triangle

Part b. Step 3. Complete the given statement.

$Δ R S T$ is an isosceles triangle

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Complete.
If $\bar{R K}$ is both an altitude and a median of $Δ R S T$ , then:
$Δ R S K ≅ Δ R T K$ by $\underline{?}$
$Δ R S T$ is $a (n) \underline{?}$ 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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Complete.IfRK¯is both an altitude and a median of ΔRST, then:ΔRSK≅ΔRTKby ?¯ΔRSTis a(n)?¯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

Statistics

Decision Maths

Probability and Statistics

Pure Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Complete.
If $\bar{R K}$ is both an altitude and a median of $Δ R S T$ , then:
$Δ R S K ≅ Δ R T K$ by $\underline{?}$
$Δ R S T$ is $a (n) \underline{?}$ triangle