Name:_____________________________________________________________ Date:_________________
Square:
Period:__________
Chapter 10: Quadrilaterals
Topic 4: Square
A square is a _________________ that has two congruent sides. A square is also a ______________ that has one right
angle.
Properties:



All of the properties of a parallelogram.
All of the properties of a rectangle.
All of the properties of a rhombus.
Word Problems:
1.) TOMA is a square. If the measure of <TOM = 3x - 9, find the value of x.
2.) ABCD is a square. If the measure of diagonal 𝐴𝐶 = 5√2, what is the length of the side?
3.) KATH is a square. If the measure of diagonal KT = 10, what is the measure of side KA? What is the
perimeter of square KATH?
4.) If one side of a square is 32 and the side opposite is 5x - 8, what is the value of x?
5.) In the accompanying diagram, ABCD is a square, diagonal BD is extended through D to E, AD ≅ DE, and AE
is drawn. What is the m<BAE?
(1) 22.5
(3) 45.0
(2) 112.5
(4) 135.0
6.) If two consecutive sides of a square are represented by 3x - 6 and x + 14, then the perimeter of the square
is
(1) 10
(2) 24
(3) 72
(4) 96
Name:_____________________________________________________________ Date:_________________
Period:__________
Square Homework Problems
Complete the following questions below.
1.) Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have
perpendicular diagonals?
(1) the rhombus, only
(3) the rhombus and the square
(2) the rectangle and the square
(4) the rectangle, the rhombus, and the square
2.) The length of the side of a square is 14. Find the length of the diagonal of the square.
3.) The length of the diagonal in a square is 26. What is the perimeter of the square? Final answer must be in
simplest radical form.
4.) Which quadrilateral is equiangular but not always equilateral?
(1) rectangle
(2) parallelogram
(3) rhombus
(4) square
5.) One side of a square is 3𝑥 − 13 and another side is 2𝑥 − 1, what is the value of x?
6.) What is the perimeter of a square whose diagonal is 3√2?
(1) 18
(2) 12
(3) 9
(4) 6
7.) In square ABCD, AC = 3x + 15 and BD = 4x – 5. Find the length of AC.
8.) In the accompanying diagram, the perimeter of ∆𝑀𝑁𝑂 is equal to the perimeter of square ABCD. If the
sides of the triangle are represented by 4x + 4, 5x – 3, and 17, and one side of the square is represented by
3x, find the length of the side of the square.
9.) What is the length of one side of the square whose perimeter has the same numerical value as its area?
(1) 5
(2) 6
(3) 3
(4) 4
Review Questions:
10.) Determine the area, in square feet, of the smallest square that contain a circle with a radius of 8 feet.
11.) The image of point (-2,3) under translation T is (3,-1). What is the image of point (4,2) under the same
translation?
(1) (-1,6)
(2) (0,7)
(3) (5,4)
(4) (9,-2)
12.) Ms. Brewer’s art class is drawing reflected images. She wants her students to draw images reflected in a
line. Which diagram represents a correctly drawn image?
13.) Which letter has point symmetry but not line symmetry?
(1) H
(2) S
(3) T
(4) X
14.) If the midpoints of the sides of a triangle are connected, the area of the triangle formed is what part of
the area of the original triangle?
(1)
1
4
(2)
1
3
(3)
3
8
(4)
1
2
15.) Rebecca’s favorite photograph has a length of 6 inches and a width of 4 inches. She wants to have it
made into a poster with dimensions that are similar to those of the photograph. She determined that the
poster should have a length of 24 inches. How many inches wide should the poster be?