# Chapter 6: Inequalities in Geometry

Q1

For the following conditional statement, classify the statement as true or false.

Q1.

Some information about the diagram is given. Tell whether the other statements can be deduced from what is given. (Write Yes or No).

Given: Point *Y* lies between points *X* and *Z*

a.$XY=\frac{1}{2}XZ$

b.$XZ=XY+YZ$

c.$XZ>XY$

d.$YZ>XY$

e.$XZ>YZ$

f.$XZ>2XY$

Q1.

An indirect proof is to be used to prove the following:

If $AB=AC$, then $\Delta ABD\cong \Delta ACD$.

Which one of the following is the correct way to begin?

a. Assume temporarily that $AB\ne AC$.

b. Assume temporarily that$\Delta ABD\ne \Delta ACD$

What is the first sentence of an indirect proof of the statement shown?

Q1.

Write (a) the contrapositive and (b) the inverse of the following statement.

If $n=17$ then $4n=68$.

Q1.

Some information about the diagram is given. Tell whether the other statements can be deduced from what is given. (Write Yes or No).

Given: Point *Y* lies between points *X* and *Z*

a. $XY=\frac{1}{2}XZ$

b. $XZ=XY+YZ$

c. $XZ>XY$

d. $YZ>XY$

e. $XZ>YZ$

f.$XZ>2XY$

Q1.

An indirect proof is to be used to prove the following:

$\text{If}AB=AC,\text{then}\Delta ABD\cong \Delta ACD$.

Which one of the following is the correct way to begin?

a. Assume temporarily that $AB\ne AC$.

b. Assume temporarily that $\Delta ABD\ne \Delta ACD$

What is the first sentence of an indirect proof of the statement shown?

Q1.

State the contrapositive of each statement

a. If I can sing, then you can dance.

b. If you can’t play baseball, then I can’t ride a horse.

c. If $x=4$, then ${x}^{2}-5=11$.

d. If $y<3$, then $y\ne 4$.

e. If a polygon is a triangle, then the sum of the measures of its angle is 180.

Q1.

Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.

If $m\angle A=50$, then $m\angle B=40$.

Q1.

Classify the following conditional as true or false.

If $j>k$, then $k<j$.

Q1.

For the following conditional statement, classify the statement as true or false.

If $3a>9$, then $a>27$.