Geometry: Concepts and Applications

Jerry Cummins, McGraw-Hill, Timothy Kanold, Margaret J. Kenney

Chapter 6

More About Triangles - all with Video Answers

Educators

Section 1

Medians

Problem 1

Explain how to draw a median of a triangle.

Jay Patel

Jay Patel

Numerade Educator

Problem 2

Draw a figure that shows three concurrent segments.

Numerade Educator

Numerade Educator

Numerade Educator

Problem 3

Kim says that the medians of a triangle are always the same length. Hector says that they are never the same length. Who is correct? Explain your reasoning.

Lauren Shelton

Numerade Educator

Problem 4

In $\triangle X Y Z, \overline{Y W}$ is a median. What is $X W$ if $X Z=17$ ?

Nidhi Singhi

Numerade Educator

Problem 5

In $\triangle A B C, \overline{B X}, \overline{C Z}$, and $\overline{A Y}$ are medians. If $A X=3 x-9$, $X C=2 x-4$, and $Z B=2 x+1$, what is $A Z$ ?

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 6

Find $E V$ if $V T=5$.

Gregory Higby

Numerade Educator

Problem 7

If $F R=20.1$, what is the measure of $\overline{V R}$ ?

Jai Chadha

Numerade Educator

Problem 8

Find $E V$ if $U V=24$.

Subhakanta Sahoo

Subhakanta Sahoo

Numerade Educator

Problem 9

If $T C=8$, find $T U$.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 10

What is $T D$ if $T V=29$ ?

Corey Bryton

Numerade Educator

Problem 11

Find the measure of $\overline{W Y}$ if $M W=22$.

Fuzail Shakir

Numerade Educator

Problem 12

What is $N W$ if $Z W=10$ ?

Manik Pulyani

Numerade Educator

Problem 13

If $P W=13$, what is $W X$ ?

Joshua Gullett

Numerade Educator

Problem 14

What is $X K$ if $G K=13.5$ ?

Grace Muhihu

Numerade Educator

Problem 15

If $F X=10.6$, what is the measure of $\overline{X J}$ ?

Shamshad Waris

Numerade Educator

Problem 16

Find $H \mathrm{X}$ if $H I=9$.

Ramzi Deek

Numerade Educator

Problem 17

If $\overline{B D}$ and $\overline{C F}$ are medians of $\triangle A B C$ and $C E=17$, what is $E F$ ?

Victor Salazar

Numerade Educator

Problem 18

In $\triangle R S T, \overline{R P}$ and $\overline{S Q}$ are medians. Find $R U$ if $U P=7.3$.

Jay Patel

Numerade Educator

Problem 19

Draw a triangle with vertices $R, S$, and $T$. Then construct the medians of the triangle to show that they are concurrent.

Raj Bala

Numerade Educator

Problem 20

Algebra In $\triangle E F G, \overline{G P}, \overline{F M}$, and $\overline{E N}$ are medians. If $E M=2 x+3$ and $M G=x+5$, what is $x$ ?

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 21

$\overline{R U}, \overline{S V}$, and $\overline{T W}$ are medians of $\triangle R S T$. What is the measure of $\overline{R W}$ if $R V=4 x+3$, $W S=5 x-1$, and $V T=2 x+9$ ?

Jay Patel

Numerade Educator

Problem 22

On a map, the points representing the towns of Sandersville, Waynesboro, and Anderson form a triangle. The point representing Thomson is the centroid of the triangle. Suppose Washington is halfway between Anderson and Sandersville, Louisville is halfway between Sandersville and Waynesboro, and the distance from Anderson to Thomson is 75 miles. What is the distance from Thomson to Louisville?

Victor Salazar

Numerade Educator

Problem 23

Thinking Draw a triangle on a piece of cardboard and cut it out. Draw only one median on the cardboard. How can you find the centroid without using the other two medians? Place the point of a pencil on the centroid you found. Does the triangle balance on your pencil? Why?

Jay Patel

Numerade Educator

Problem 24

In $\triangle M N P$ and $\triangle R S T$, $\angle M \cong \angle R$ and $\overline{M P} \cong \overline{R T}$.
Name the additional congruent angles needed to show that the triangles are congruent by ASA.

Amrita Bhasin

Numerade Educator

Problem 25

In $\triangle D E F$ and $\triangle G H J, \overline{D E} \cong \overline{G H}$, $\overline{E F} \cong \overline{H J}$, and $\angle F \cong \angle J$. Tell whether the triangles are congruent by SAS. Explain.

Dale Sanford

Numerade Educator

Problem 26

A rower is designed to simulate rowing. In the diagram shown, notice that the base of the rower, along with the lower portion of the oar, and the hydraulic resistance bar form a triangle. Suppose the measures of two of the angles are 15 and 100 . What is the measure of the third angle?

Mike Gaerlan

Numerade Educator

Problem 27

In the equation $y=5 x+3, y$ represents the total cost of a trip to the aquarium for $x$ people in a car. Name the slope and $y$-intercept of the graph of the equation and explain what each value represents.

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 28

Find $x$ so that $a \| b$.

Taylor Shimono

Numerade Educator

Problem 29

The toaster shown at the right is formed by a series of intersecting planes. Which names a pair of skew segments? (Lesson 4-1)
(A) $\overline{B C}$ and $\overline{E F}$
(B) $\overline{B E}$ and $\overline{C H}$
(C) $\overline{C D}$ and $\overline{D G}$
(D) $\overline{E H}$ and $\overline{A D}$

Martha Richards

Martha Richards

Numerade Educator