Math in Focus Grade 7 Chapter 7 Review Test Answer Key

Practice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 7 Review Test to score better marks in the exam.

Math in Focus Grade 7 Course 2 B Chapter 7 Review Test Answer Key

Concepts and Skills

Construct the angle bisector of ∠ABC on a copy of each figure using a compass and straightedge.

Question 1.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 1
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-1

 

 

 

 

 

 

Question 2.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 2
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-2

 

 

 

 

 

 

Use a protractor to draw an angle with the given measure. Then use a compass and straightedge to construct its angle bisector.

Question 3.
m∠XYZ = 37°
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-2

 

 

 

 

 

Question 4.
m∠PQR = 72°
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-2

 

 

 

 

 

 

Question 5.
m∠KLM = 128°
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-5

 

 

 

 

 

 

On a copy of each angle, construct the angle with the given measure by constructing the angle bisector. Use only a compass and straightedge.

Question 6.
Construct a 65° angle whose vertex is point X.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 3
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-3

 

 

 

 

 

Question 7.
Construct a 66° angle whose vertex is point Y.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 4
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-4

 

 

 

 

 

 

 

Draw a line segment with the given length. Then construct the perpendicular bisector of the segment using a compass and straightedge.

Question 8.
AB = 6.5 cm
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-6

 

 

 

 

 

 

 

Question 9.
CD = 4.5 cm
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-7

 

 

 

 

 

 

 

Question 10.
AD = 10.8 cm
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-8

 

 

 

 

 

 

 

On a copy of the figure shown, using only a compass and straightedge, draw the perpendicular bisectors of \(\overline{\mathbf{P Q}}\) and \(\overline{\mathbf{P R}}\). Label the point where the two perpendicular bisectors intersect as W.

Question 11.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 5
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-9

 

 

 

 

 

 

Question 12.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 6
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-6

 

 

 

 

 

Use the given information to find the number of triangles that can be constructed. Try constructing the triangles to make your decision.

Question 13.
Triangle WXY: WX = 4.5 cm, m∠XWY = 60°, and m∠WXY = 40°.
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-13

 

 

 

 

 

Question 14.
Triangle ABC: AB = 5 cm, AC = 4.5 cm, and m∠CAB = 60°.
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-14

 

 

 

 

 

Question 15.
Triangle DEF: DE = 4 cm, EF = 3 cm, and DF = 8 cm.
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-15

 

 

 

 

 

 

Use the given information to construct each quadrilateral.

Question 16.
Rhombus DEFG with diagonal DF = 4.2 cm and DE = 5 cm.
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-15

 

 

 

 

 

 

Question 17.
Parallelogram ABCD with AB = 7 cm, DA = 4.5 cm, and m∠ABC = 50°.
Answer:
Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-16

 

 

 

 

 

 

Question 18.
Quadrilateral ABCD such that AB = 5 cm, AD = 3.5 cm, BC = 4 cm, m∠BAD = 60°, and m∠ABC = 90°.
Answer:

Math-in-Focus-Grade-7-Chapter-7-Review-Test-Answer-Key-17

 

 

 

 

 

 

 

 

Solve. Show your work.

Question 19.
A rectangular garden is 15 meters long and 9 meters wide. Use a scale of 1 centimeter to 3 meters, make a scale drawing of the garden.
Answer:
length of the garden is = 45 m
width of the garden is = 27 m

Explanation:
Given the length of the rectangle = 15m
Breadth of the rectangle = 9 m
given scale as 1 centimeter = 3 m
The new length of the garden is = 15 × 3 = 45 m
New breadth of the garden is = 9 × 3 = 27 m

Question 20.
The scale of the floor plan of a room is 1 inch: 6.5 feet. On the floor plan, the room is 8 inches long and 6 inches wide. What are the actual dimensions of the room?
Answer:
1 inch : 6.5 feet means 1 inch on the map represents 6.5 feet on the ground.
Let’s note:
x cm = the actuaL Length
y cm = the actual width.
We have:
1 in. : 6.5 ft = 8 in. : x ft = 6 in. : y ft
Write ratios in fraction form:
\(\frac{1 \mathrm{in} .}{6.5 \mathrm{ft}}=\frac{8 \mathrm{in} .}{x \mathrm{ft}}=\frac{6 \mathrm{in} .}{y \mathrm{ft}}\)
Write without units:
\(\frac{1}{6.5}\) = \(\frac{8}{x}\) = \(\frac{6}{y}\)
Write cross products:
x = 8 · 6.5
y = 6 · 6.5
Simplify
x = 52 ft
y = 39 ft
The actual dimensions of the room are 52 ft and 39 ft.

Question 21.
A model of a car is made using the scale 1 : 25. The actual length of the car is 4.8 meters. Calculate the length of the model of the car in centimeters.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 7
Answer:
1 : 25 means 1 cm on the map represents 25 cm on the ground.
Let x inches be the Length of the car on the map.
We have:
4.8 cm = 4.8 · 100 cm = 480 cm
1 cm : 25 cm = x cm : 480 cm
Write ratios in fraction form:
\(\frac{1 \mathrm{~cm}}{25 \mathrm{~cm}}\) = \(\frac{x \mathrm{~cm}}{480 \mathrm{~cm}}\)
Write without units:
\(\frac{1}{25}\) = \(\frac{x}{480}\)
Write cross products:
25x = 480
Divide both sides by 25:
\(\frac{25x}{25}\) = \(\frac{480}{25}\)
Simplify:
x = 19.2
On the map, the car’s length is 19.2 cm.

Question 22.
The scale on a map is 1 inch : 120 miles. On the map, a highway is 5 inches long. Find the actual length of the highway in miles.
Answer:
Length = 24 miles

Explanation:
Scale on a map is 1 inch: 120 miles
The highway is 5 inches.
The actual length of the highway in miles is 1 × \(\frac{120}{5}\)
length of the highway is 24 miles.

Problem Solving

Solve.

Question 23.
Joe constructed an isosceles triangle WXY such that VVX = WY = 5 cm and XY = 4 cm. Construct another isosceles triangle ABC such that AB = AC = 10 cm and BC = 8 cm. Is triangle ABC an enlargement or a reduction of triangle WXY? Explain your answer and give the scale factor. Justify your answer.
Answer:
We are given △WXY and △ABC:
WX = WY = 5
XY = 4
AB = AC = 10
BC = 8
We construct △WXY:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 1
We construct △ABC:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 2
The sides of △ABC have twice the lengths of the sides of △WXY. Therefore △ABC is an enlargement of △WXY. The scale factor is 2.

Question 24.
James was asked to design a square decorative tile with a side length of 90 millimeters. Construct the square on which James will draw his design.
Answer:
We have to construct the square:
AB = 90 mm
Sketch the square:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 3
Use a ruler to draw \(\overline{A B}\) so that is 90 mm long:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 4
Using a protractor, draw ∠A and ∠B with a measure of 90°.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 5

Because AD = BC = 90 mm, set the compass to a radius of 90 mm. Then using A and B as the center, draw two arcs intersecting the rays drawn in the previous step. Label these points of intersection as D and C.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 6
Draw \(\overline{C D}\).
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 7

Question 25.
Harry is designing a theater platform in the shape of a rhombus using a blueprint. The lengths of the diagonals on his blueprint are 4 centimeters and 9 centimeters. Construct the rhombus. Then measure a side length. If the scale of the drawing is 1 centimeter: 2 meters, about what length of skirting does Harry need to go around all four edges of the platform?
Answer:
We are given the rhombus:
AC = 9
BD = 4
We draw the segment of length 20 and label it BD:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 8
We bisect the segment \(\overline{A C}\).
Place the compass point at A. Then draw an arc on each side of \(\overline{A C}\) with a radius greater than half of the length of \(\overline{A C}\).
Using the same radius, set the compass point in C. Draw one arc on each side of \(\overline{A C}\).
Label the points where the arcs intersect as E and F.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 9
Use a straightedge to draw a line through E and F. Label the intersection point of \(\overline{E F}\) and \(\overline{A C}\) by O.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 10

As rhombus diagonals bisect each other, point O is the middle point of \(\overline{B D}\). Place the compass point at O.Then draw an arc on each side of \(\overline{A C}\) with a radius \(\frac{4}{2}\) = 2cm. Label the intersections of these arcs with \(\overline{E F}\) by B and D.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 11
Use a ruler to draw AB, BC, CD, DA.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 12
Measure a side of the rhombus:
AB ≈ 4.9 cm
We are given the scale:
1 cm : 2 m
Let’s note by r the actual length of one side of the rhombus.
\(\frac{1}{2}\) = \(\frac{4.9}{x}\)
We determine x:
x = 2 49
x = 9.8 m
Calculate the perimeter of the rhombus:
4 · 9.8 = 39.2 m

Question 26.
Michael wants to make some kites out of a plastic sheet for a family picnic. Before making the kites he wants to make a \(\frac{1}{4}\) scale model to find the lengths and angles needed for each kite. The diagram shows the measurements of the actual kite. He knows that \(\overline{A C}\) is the perpendicular bisector of \(\overline{B D}\), and that \(\overline{A N}\) should be 6 inches long. Construct the model he will use and find the measures of ∠ABC and the lengths AB and BC in the actual kite.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key 8
Answer:
We are given the actual kite dimensions:
AC = 24
BD = 20
AN = 6
Determine the dimensions of the model kite:
\(\frac{1}{4}=\frac{A^{\prime} C^{\prime}}{A C}=\frac{B^{\prime} D^{\prime}}{B D}=\frac{A^{\prime} N^{\prime}}{A N}\)
\(\frac{1}{4}=\frac{A^{\prime} C^{\prime}}{24}=\frac{B^{\prime} D^{\prime}}{20}=\frac{A^{\prime} N^{\prime}}{6}\)
4A’C” = 24 ⇒ A’C” = 6
4B’D’ = 20 ⇒ B’D’ = 5
4A’N’ = 6 ⇒ A’N’ = 1.5
We draw the segment of length 5 and label it B’D’:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 13

We bisect the segment \(\overline{B^{\prime} D^{\prime}}\).
Place the compass point at B’. Then draw an arc on each side of \(\overline{B^{\prime} D^{\prime}}\) with a radius greater than half of the length of \(\overline{B^{\prime} D^{\prime}}\).
Using the same radius, set the compass point in D’. Draw one arc on each side of \(\overline{B^{\prime} D^{\prime}}\).
Label the points where the arcs intersect as E and F
Use a straightedge to draw a line through E and F. Label the intersection point of \(\overline{E F}\)
and \(\overline{B^{\prime} D^{\prime}}\) by N’.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 14
Place the compass point at N’. With a radius of 1.5 in. draw an arc above \(\overline{B^{\prime} D^{\prime}}\). Label the intersection of this arc with \(\overline{E F}\) by A’.
Place the compass point at N’. With a radius of 6 – 1.5 = 4.5 in. draw an arc below \(\overline{B^{\prime} D^{\prime}}\). Label the intersection of this arc with \(\overline{E F}\) by C”.
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 15
Use a ruler to draw A’B’, B’C”, C”D’, D’A’.
Measure a side of the rhombus:
Math in Focus Grade 7 Chapter 7 Review Test Answer Key A 16
Measure ∠ABC:
m∠ABC ≈ 93°
Measure the length5 A’B’ and B’C” in the model kite:
A’B’ ≈ 2.9 in.
B’C” ≈ 5.1 in.
Determine the Lengths AB and BC in the actual kite:
\(\frac{1}{4}=\frac{A^{\prime} B^{\prime}}{A B}=\frac{B^{\prime} C^{\prime}}{B C}\)
\(\frac{1}{4}=\frac{2.9}{A B}=\frac{5.1}{B C}\)
AB = 4 · 2.9 = 11.6 in.
BC = 4 · 5.1 = 20.4 in.

Question 27.
The scale of a map is 1 inch to 5 feet. Find the area of a rectangular region on the map if the area of the actual region is 95 square feet.
Answer:
The area of a rectangular region is 19 square inches.

Explanation:
The scale of a map is 1 inch to 5 feet.
The area of the actual region is 95 square feet.
The area of a rectangular region is = 95 × \(\frac{1}{5}\)
Area of rectangle is = 19 sqaure inches.

Question 28.
The floor plan of a building has a scale of \(\frac{1}{4}\) inch to 1 foot. A room has an area of 40 square inches on the floor plan. What is the actual room area in square feet?
Answer:
10 square feet.

Explanation:
The floor plan of a building has a scale of \(\frac{1}{4}\) inch to 1 foot.
A room has an area of 40 square inches.
The actual room area in square feet is 1× \(\frac{40}{4}\)
= 10 sqaure feet.

Question 29.
The scale of a map is 1 : 2,400. If a rectangular piece of property measures 2 inches by 3 inches on the map, what is the actual area of this piece of property to the nearest tenth of an acre? (1 acre = 43,560 ft2)
Answer:
1: 2,400 means 1 inch on the map represents 2,400 inches on the ground.
Map length : Actual length = 1 in. : 2,400 in.
Map area: Actual area = 1 in.2 : 2. 4002 in.2
Let y represent the actual area of the rectangle in square inches.
Write a proportion:
\(\frac{\text { Area of rectangle on map }}{\text { Actual area of rectangle }}=\frac{1}{5,760,000}\)
Substitute:
\(\frac{2 \cdot 3}{y}\) = \(\frac{1}{5,760,000}\)
Write the cross products:
y = 6 · 5.760,000
Simplify:
y = 34,560,000 in.2
We convert the actual area to acres:
1 acre = 43,560 ft2 = 43,460 · 122 in.2
= 6,258,240 in.2
\(\frac{34,560,000}{6,258,240}\) ≈ 5.52 acres

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