Practice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 7 Lesson 7.4 Constructing Quadrilaterals to score better marks in the exam.

## Math in Focus Grade 7 Course 2 B Chapter 7 Lesson 7.4 Answer Key Constructing Quadrilaterals

### Math in Focus Grade 7 Chapter 7 Lesson 7.4 Guided Practice Answer Key

Construct the quadrilateral from the given dimension. Use a ruler and protractor.

Question 1.
Rectangle ABCD measuring 7 centimeters by 5 centimeters.
Explanation:

we have drawn the rectangle with the measurements of length=5cm and breadth=7cm.

Construct the quadrilateral from the given information. Use a compass, ruler, and protractor.

Question 2.
Parallelogram KLMN: KL = 6.4 cm, LM = 4.8 cm, and m∠KLM = 60°.
Explanation:

The measurements of the parallelogram of length= 4.8cm and breadth=6.4cm. The angle of KLM=60.

Construct the quadrilateral from the given
information. Use a ruler, compass, and protractor.

Question 3.
Rhombus PQRS with diagonal PR = 6.2 cm and PQ = 4.5 cm.
Explanation:

we drawn the rhombus with the measurement angels of PR=6.2cm and PQ=4.5cm.

### Math in Focus Course 2B Practice 7.4 Answer Key

Construct each quadrilateral from the given information.

Question 1.
Rectangle KLMN measuring 5.3 centimeters by 4.7 centimeters.
The measuring angles of rectangle is Length = 5.3 cm and breadth= 4.7 cm

Explanation:

Question 2.
Square with side lengths of 7 centimeters.
Explanation:

The measuring angles of the square is 7cm.

Question 3.
Rhombus DEFG with diagonal DF = 6 cm and DE = 4.5 cm.
Explanation:

The measuring angles of the rhombus DEFG diagonals DF=6cm and DE=4.5cm.

Question 4.
Parallelogram PQRS with PQ = 3.8 cm, QR = 5 cm, and m∠QPS = 70°.
Explanation:

The measuring angles of the parallelogram PQRS
PQ=3.8cm and QR=5cm
we got the angle 70°.

Question 5.
Quadrilateral ABCD with AB = 6.7 cm, BC = 7.2 cm, AD = 4.9 cm, CD = 6.2 cm, and m∠ABC = 55°.
Explanation:

The measurements of quadrilateral ABCD of AB = 6.7, BC = 7.2, CD = 6.2 and DA = 4.9. We got the angle ABC = 55°.

Question 6.
Construct quadrilateral ABCD with diagonal AC = 5 cm, AB = CD = 4 cm, BC = 6 cm, and AD = 6 cm.
Explanation:

The measurements of the rectangular quadrilateral is AB = CD = 4cm , BC and AD = 6cm. The diagonal AC = 5cm. So this is a quadrilateral rectangular.

First we construct △ABC.
Use a ruler to draw the segment 6 cm long. Label its endpoints by B and C.

Because AB = 4 cm, use the ruler to set the compass to a radius of 4 cm. Then using B as center draw an arc of radius 4 cm above $$\overline{B C}$$.

Because AC = 5 cm, use the ruler to set the compass to a radius of 5 cm. Then using C as center draw an arc of radius 5 cm that intersects the first arc. Label the intersection as A.

Use the ruler to draw $$\overline{A B}$$ and $$\overline{A C}$$.

Then we construct △ACD.
Because AD = 6 cm, use the ruler to set the compass to a radius of 6 cm. Then using A as center draw an arc of radius 6cm above $$\overline{A C}$$.

Because CD = 4 cm, use the ruler to set the compass to a radius of 4 cm. Then using C as center draw an arc of radius 4 cm that intersects the first arc. Label the intersection as D.

Use the ruler to draw $$\overline{A D}$$ and $$\overline{C D}$$.

The quadrilateral ABCD is rectangle because the angles AB and CD are equal with the  =4cm and the angles BC and AD are equal with the = 6cm. So this is rectangular quadrilateral.

b) Draw $$\overline{B D}$$ to intersect $$\overline{A C}$$ at point E. Find the lengths of $$\overline{A E}$$, $$\overline{C E}$$, $$\overline{B E}$$, and $$\overline{D E}$$.
Draw $$\overline{B D}$$

We measure AE, CE, BE, DE:
AE = 2.5
CE = 2.5
BE = 4.4
DE = 4.4

c) Do the diagonals $$\overline{A C}$$ and $$\overline{B D}$$ bisect each other? Justify your answer.
The diagonals $$\overline{A C}$$ and $$\overline{B D}$$ bisect each other This is explained by the fact that the quadrilateral is a parallelogram.

Question 7.
Construct a quadrilateral STUV by following Steps 1 to 5.
STEP1
Draw $$\overline{S T}$$ so that ST = 5 cm.
STEP 2
With T as the center, draw $$\overline{T U}$$ perpendicular to $$\overline{S T}$$ , with TU = 4 cm.
STEP 3
With U as the center, draw an arc of radius 5 centimeters.
STEP 4
With S as the center, draw an arc of radius 4 centimeters to intersect the arc drawn in Step 3. Label this point of intersection as V.
STEP 5
Complete the construction of quadrilateral STUV.
Use a ruler to draw $$\overline{S T}$$ so that is 5 cm long.

Using a protractor, draw ∠T with a measure of 90°.

Because TU = 4 cm, set the compass to a radius of 4 cm. Then using T as the center, draw an arc intersecting the ray drawn in previous step. Label this point of intersection as U.

With U as center, draw an arc of radius 5 cm.
With S as center, draw an arc of radius 4 cm to intersect the arc drawn in the previous step. Label this point of intersection as V.

Draw $$\overline{V U}$$ and $$\overline{V S}$$.

a) Find each of the angles in quadrilateral STUV.
We measure the angles of the quadrilateral:
m∠T = 90°
m∠U = 90°
m∠V = 90°
m∠S = 90°

As all angles are right angles, the quadrilateral is a rectangle.

c) Find the lengths of the diagonals. What do you notice?
We find the lengths of the diagonals:
SU ≈ 6.4
VT ≈ 6.4

The diagonals are congruent.

Question 8.
Construct a quadrilateral ABCD with all sides of length 3 centimeters and diagonal BD = 5.2 cm.
Explanation:

The quadrilateral ABCD is a square because the sides of the square AB, BC, CD  and DA are equal with 3 cm and the diagonal BD=5.2cm.

b) Find the measure of each of the angles formed by the intersection of the diagonals.
The measuring of each of the angles formed by the intersection of the diagonals is acute angle 60°.

Question 9.
Construct quadrilateral ABCD with diagonal AC = 6 cm, AB = 3 cm, BC = 4 cm, CD = 4.5 cm, and AD = 9 cm. What type of quadrilateral does ABCD seem to be? Explain your reasoning.
Explanation:

The quadrilateral ABCD is trapezoid. AB=3cm ,BC=4cm,CD=4.5cm and DA=9cm.
The diagonal AC = 6cm.So this is trapezoid.

Question 10.
Construct the figure below using the given dimensions.

Use a ruler to draw $$\overline{A B}$$ so that is 6.6 cm long.

Using a protractor, draw ∠B with a measure of 90° and ∠A with a measure of 90°.

Because AD = BC = 3.4 cm, set the compass to a radius of 3.4 cm. Then using A and B as centers, draw arcs intersecting the rays drawn in previous step. Label this points of intersection as D and C.

Because AE = EC = 4 cm, set the compass to a radius of 4 cm. Then using C and D as centers, draw arcs above $$\overline{C D}$$. Label the point of intersection of the two arcs as E.

Draw $$\overline{E D}$$ and $$\overline{E C}$$.

Question 11.
a) Construct quadrilateral ABCD with AB = 6 cm, BC = 3 cm, AD = 4 cm, m ∠BAD = 120°, and m ∠ABC = 100°.
Explanation:

The measurements of the quadrilateral ABCD is AB=6cm , BC=3cm , AD =4cm. The angle BAD= 120° angle ABC =100°.

b) Find the length of $$\overline{C D}$$.
The length of overline CD=10cm.

c) Label the midpoints of the four sides of this quadrilateral as W, X, Y, and Z. Join them to form quadrilateral WXYZ.
Explanation:

d) Compare the lengths of $$\overline{W X}$$ and $$\overline{Y Z}$$ . Compare the lengths of $$\overline{X Y}$$ and $$\overline{W Z}$$. What do you notice?
Measure WX, YZ, XY, WZ:
WX ≈ 3.6 cm
YZ ≈ 3.6 cm
XY ≈ 4.4 cm
WZ ≈ 4.4 cm
We notice that we have:
WX = YZ
XY = WZ

Question 12.
Construct parallelogram PQRS with PQ = 6 cm, a height of 4.5 centimeters and interior angles 45° and 135°.
Explanation:

The measurements of the parallelogram PQRS with PQ =6cm and height= 4.5cm.
The interior angles are  45° and 135°.

Question 13.
Draw rhombus ABCD with AC = 5 cm and AB = 6.5 cm. Also draw diagonal $$\overline{B D}$$. How are the two diagonals related to each other? Explain.
Explanation:

let ABCD be a rhombus whose diagonal AC and BD are intersecting at point O. We know that the diagram of parallelogram bisect at each other.
OA=OC and OB=OD
angle COB= angle COD
angle COB+ angle COD= 180°
angle COB=angle COD= 90°.

Question 14.
Jenny plans to make a trapezoidal bookmark for each of her teachers. The top will be 5 centimeters long and have right angles at either end. The right side will be 12 centimeters long, and the bottom of the bookmark will make a 50° angle with this side. Construct a template for Jenny’s bookmark. How long is the left side of Jenny’s template to the nearest centimeter?
Explanation:

The measurements of the trapezoid length is 5cm and breadth is 12 cm. The bottom of the book mark angle is  50°. The left side of the jenny’s template is 4cm.

Question 15.
Martha plans to cut squares of paper from a roll of wrapping paper. She will package the squares to sell as origami papers to raise funds for a charity. If the area of the square paper is 64 square centimeters, construct the square Martha can use as a template.
Determine the length of the square side:
AB2 = 64
AB = $$\sqrt{64}$$ = 8
Sketch the rectangle:

Use a ruler to draw $$\overline{A B}$$ so that is 7 cm long.

Using a protractor, draw ∠B with a measure of 90°.

Because BC = 5 cm, set the compass to a radius of 5 cm. Then using B as the center, draw an arc intersecting the ray drawn in previous step. Label this point of intersection as C. Because AD = 5 cm, use the same compass setting. Using A as the center, draw an arc:

Because CD = 7 cm, set the compass to a radius of 7 cm. Then using C as the center draw an arc intersecting the ray drawn in previous step. Label this point of intersection as D.

Draw $$\overline{C D}$$ and $$\overline{A D}$$

Question 16.
Jessie plans to make a patchwork pattern from colored paper by repeating a rhombus whose diagonals measure 4 centimeters and 5 centimeters. Use the given dimensions to construct a template for the rhombus.
We have to construct the rhombus ABCD.
AC = 4
BD = 5
Sketch the rhombus:
Use a ruler to draw $$\overline{A C}$$ so that is 4 cm long.

Draw the perpendicular bisector of $$\overline{A C}$$:

Because OB = OD = $$\frac{5}{2}$$ = 2.5 cm, use the compass setting 2.5 cm. Then using O as the center, draw an arc to intersect the perpendicular bisector in the points B and D.

Draw $$\overline{A B}$$, $$\overline{B C}$$, $$\overline{C D}$$ and $$\overline{D A}$$.