Free Practical Geometry 01 Practice Test - 8th Grade

During the construction of a quadrilateral for which 2 sides and 3 angles are known, how is the 4th point plotted?

A.

Using only length

B.

Using angle and length

C.

Using 2 angles

D.

Using arcs

SOLUTION

Solution : C

Suppose, we need to construct a triangle of whose two given sides are 'a' cm and 'b' cm and three given angles are x, y and z.

Step 1: Draw PQ = a cm.

Step 2: Construct angle measuring x° at point Q.

Step 3: with Q as centre and radius equal to b cm cut an arc to meet at R.

Step 4: Construct an angle measuring y° at point R.

Step 5: Construct an angle measuring z° at P.

Step 6: The point of intersection of both the lines is the required point. Let this point be S.

Thus, fourth point is plotted using lines made by any two angles.

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = 70, Angle Q = 100, Angle R = 80 and Angle S =80.

A.

0

B.

1

C.

2

D.

Infinite

SOLUTION

Solution : D

From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to fix points R and S. Hence, infinite quadrilaterals can be drawn fixing points P and Q wherever required according to angles R and S.

I construct quadrilateral with 3 sides and 2 included angles being 75 and 105 respectively and no sides are  equal.  What is the type of quadrilateral I am constructing?

A.

Parallelogram

B.

Trapezium

C.

Square

D.

Rhombus

SOLUTION

Solution : B

The given is 3 sides and 2 included angles
The angles are adjacent angles
Also their sum is 75+105=180
Given angles are supplementary.
Then the remaining two angles are also supplementary.  [ Sum of all the angles of a quadrilateral is 3600]
Hence, the quadrilateral is a trapezium as in a trapezium  adjacent angles are supplementary angles and since its given no sides are equal , it cannot be a parallelogram( opposite sides are equal) and square, rhombus( all sides are equal)

To construct a quadrilateral using triangles, minimum number of triangles needed are

A.

1

B.

2

C.

3

D.

4

SOLUTION

Solution : B

2 triangles are needed to construct a quadrilateral. The triangles will have the diagonal as common side.

If a quadrilateral with 4 sides and a diagonal is given, which of the following conditions is used in the construction?

A.

SSS

B.

SAS

C.

ASA

D.

AAS

SOLUTION

Solution : A

A quadrilateral is made up of two triangles. Diagonal is the common side for both the triangles. If all the four sides and a diagonal is known, then we can construct a quadrilateral by constructing two triangles. The two triangles are constructed using SSS property.

If I have a quadrilateral PQRS, how many triangles are there in the quadrilateral in which I must have one of the diagonals as a side.

A.

1

B.

2

C.

3

D.

4

SOLUTION

Solution : D

Consider quadrilateral ABCD above. The triangles that can be constructed with diagonals are the following- ABC, DBC, BAD, CAD. Hence, 4 triangles are possible.

If I combine 2 equilateral triangles along a side, what quadrilateral do I get?

A.

Rhombus

B.

Square

C.

Rectangle

D.

Parallelogram

SOLUTION

Solution : A

If I combine 2 equilateral triangles, I get a quadrilateral with all sides equal. Since the angle of an equilateral triangle is 60, no sides will be perpendicular. The quadrilateral formed cannot be a square. Hence, it is a rhombus.

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, Angle M = 75, Angle I = 105 and Angle S = 120. Which line segment should be drawn first?

A.

ST

B.

IS

C.

IM

D.

TM

SOLUTION

Solution : B and C

The line segment for which both the angles are given should be drawn first. For e.g. in the case of line segment MI, both angles M and I are known. Similarly, for IS, the angle I and S are known. Thus, either MI or IS can be drawn, because angles at both end points of both line segments are known.

In the construction of quadrilateral ABCD, AB, BC, CD, AC and BD are given. Which of the following triangles cannot be drawn as the first step of construction?

A.

ABC

B.

C.

BCD

D.

ABD

SOLUTION

Solution : B and D

As no angles are given, we need to know all three sides to construct a triangle. Thus, triangle ADC and ABD cannot be constructed as first step because side AD’s length is not known.

A quadrilateral is constructed using 2 congruent triangles. Two of its sides are 2 and 3 units. What are the possible values of the 3rd side?

A.

1<3rd side<5 units

B.

13rd side<5 units

C.

13rd side5 units

D.

1<3rd side5 units

SOLUTION

Solution : A

Sum of the two sides of the triangle is greater than 3rd side
let, 1st side be a=2, 2nd be b=3, 3rd be c.
As per above condition,
a+b>c 2+3>c  c<5
a+c>b 2+c>3  c>1
so, 1<c<5 units