﻿ Geometry Worksheets | Problems & Solutions

# Geometry Worksheets

Geometry Worksheets
• Page 1
1.
Name the property which is used to solve the equation $x$ + 21 = 24 .
 a. addition property b. subtraction property c. distributive property d. substitution property

#### Solution:

x + 21 = 24
[Given equation.]

x + 21 - 21 = 24 - 21
[Subtraction property.]

x = 3
[Simplify.]

So, subtraction property is used to solve the equation.

2.
Which will always be equal?
 a. Complementary angles b. Vertical angles c. Adjacent angles d. Supplementary angles

#### Solution:

Vertical angles are congruent.
[Vertical Angles Theorem.]

3.
Find the value of $x$.

 a. 1 b. 7 c. 15.4 d. 14

#### Solution:

8x + 4 + 3x + 9 = 90

11x + 13 = 90

11x + 13 - 13 = 90 - 13
[Subtraction property.]

11x = 77
[Simplify.]

x = 7
[Apply division property by dividing both sides with 11.]

4.
Two coplanar angles with a common side, a common vertex and no common interior points are called
 a. complementary angles b. supplementary angles c. vertical angles d. adjacent angles

#### Solution:

Two coplanar angles with a common side, a common vertex and no common interior points are called Adjacent angles.

5.
If $m$$\angle$$A$ = $m$$\angle$$B$, then which is the correct expression of the subtraction property of equality?
 a. $m$$\angle$$A$ - $m$$\angle$$B$ = 0 b. $m$$\angle$$A$ + $m$$\angle$C = $m$$\angle$$B$ + $m$$\angle$$C$ c. $m$$\angle$$A$ + $m$$\angle$$B$ = 180 d. $m$$\angle$$A$ - $m$$\angle$$B$ = $m$$\angle$$A$ - $m$$\angle$$C$

#### Solution:

'If mA = mB, then mA - mB = mA - mC' - Here, same quantity is not subtracted.

'If mA = mB, then mA + mC = mB + mC' - Here, same quantity is added.

If mA = mB then mA + mB = 180 does not represent the subtraction property.

' mA = mB, then mA - mB = mB - mB'
[Subtract mB from both sides.]

mA - mB = 0

So, 'If mA = mB, then mA - mB = 0 ' shows subtraction property.

6.
Select addition property for $m$$\angle$X = $m$$\angle$Y.
 a. $m$$\angle$X - $m$$\angle$A = $m$$\angle$Y + $m$$\angle$A b. ($m$$\angle$X)2 = ($m$$\angle$Y)2 c. $m$$\angle$X$m$$\angle$Y + $m$$\angle$A = $m$$\angle$X$m$$\angle$Y + $m$$\angle$B d. $m$$\angle$X + $m$$\angle$Y = 2$m$$\angle$Y

#### Solution:

'mXmY + mA = mXmY + mB' - Different quantities are added.

'mX - mA = mY + mA' - Same quantity added to one side and subtracted from the other side.

'(mX)2 = (mY)2' - Both the sides are squared.

'mX + mY = mY + mY'

'mX + mY = 2mY '
[Simplify.]

'mX + mY = 2mY ' represents addition property.

7.
Name the property that justifies the statement. If $\stackrel{‾}{\mathrm{AB}}$ $\cong$ $\stackrel{‾}{\mathrm{PQ}}$, then $\stackrel{‾}{\mathrm{PQ}}$ $\cong$ $\stackrel{‾}{\mathrm{AB}}$.
 a. transitive property b. substitution property c. reflexive property of congruence d. symmetric property of congruence

#### Solution:

The property that justifies the statement: "AB PQ, then PQ AB" is the symmetric property of congruence.

8.
Select the correct statement / statements.
I. If $x$ = 9, then 5$x$ = 45 justifies multiplication property.
II. 3$x$ - 24 = 9 can be solved by addition property alone.
III. If $x$ = 2$y$, then 5$x$ - 7 = 5$y$ - 7 by substitution property.
 a. II only b. I, II, and III c. I only d. I, and II only

#### Solution:

If x = 9, then 5x = 5 · 9 = 45
[Multiplication Property.]

3x - 24 = 9
[Given equation.]

3x - 24 + 24 = 9 + 24

3x = 33
[Simplify.]

Addition alone cannot solve for x.

If x = 2y, then 5x - 7 = 10y - 7

Only statement I is correct.

9.
Select the order in which different properties are used to solve for $x$ and $y$ from the equations:
$x$ = $y$
3$x$ + $y$ - 10 = 14
 a. Addition, Division, and Substitution b. Addition and Division c. Substitution, Subtraction, and Division d. Substitution, Addition, and Division

#### Solution:

x = y,
3x + y - 10 = 14

[Given equations.]

3x + x - 10 = 14
[Substitute y = x in second equation.]

4x - 10 = 14
[Simplify.]

4x - 10 + 10 = 14 + 10

4x = 24
[Simplify.]

x = 6
[Divide both sides by 4.]

The properties used are Substitution, Addition, and Division in the same order.

10.
If $x$ + 5$y$ = 2 and $x$ = $y$, then it can be proved that 18$x$ + 7 = 13 using the property of
(i) substitution
(iii) division
(iv) subtraction
(v) multiplication
 a. (ii) and (iv) b. (i), (ii), and (iii) c. (i), (v), and (ii) d. (i), (iii), and (iv)

#### Solution:

If x = y, then x can replace y in any expression.
[Substitution Property.]

x + 5y = 2 can be written as x + 5x = 2
[Substitution property.]

6x = 2
[Simplify.]

18x = 6
[Multiply both sides by 3 - Multiplication property.]

18x + 7 = 6 + 7