Practical Geometry(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

PRACTICAL GEOMETRY MCQs

Total Questions : 105 | Page 8 of 11 pages

Question 71.

Which of the following options is/are correct when a transversal intersects two parallel lines?

Corresponding angles are equal.
Alternate interior angles are equal.
Vertically opposite angles are equal.
Complementary angles are equal.

Discuss Question

Answer: Option A. -> Corresponding angles are equal.
:
A, B, and C

If two lines are parallel then:

Corresponding angles are equal i.e., $∠ a = ∠ e$

Alternate interior angles are equal i.e., $∠ c = ∠ f$

Alternate exterior angles are equal i.e., $∠ b = ∠ g$

Vertically opposite angles are equal in case of intersecting lines.
Two angles are complementary when they add up to 90 degrees.

Question 72.

Statement $1$ : When two lines intersect each other, only the angles forming linear pair are supplementary.

Statement $2$ : When two lines intersect each other, angles forming linear pair are supplementary.

Choose the correct option.

Both the statements are correct.
Statement $1$ is correct but statement $2$ is incorrect.
Statement $2$ is correct but statement $1$ is incorrect.
Both the statements are incorrect.

Discuss Question

Answer: Option C. -> Statement

2

is correct but statement

1

is incorrect.
:
C

Statement $2$ is correct while statement $1$ is incorrect.
Reason:-If the lines are perpendicular to each other, then the pair of vertically opposite angles are also supplementary.

Question 73.

$If there are four line segments of length3cm, 7cm, 14cm and 21cm. Then how many triangles can be drawn from these line segments?$

Discuss Question

Answer: Option C. -> Statement

2

is correct but statement

1

is incorrect.
:

The condition to form a triangle is that sum of the lengths of two sides of a triangle must be greater than the third one.
Consider 3 cm , 7 cm and 14 cm ;
3 + 7 $≯$ 14 cm
Similarily if we consider other combination 7 ,14 ,21 , 14 + 21 $≯$ 7
Hence no triangles can be formed.

Question 74.

You are given the measurement of two sides of a right angled triangle such that these sides enclose the right angle. What else do you need in order to draw a triangle?

Length of the third side
Measure of one angle
Either length of one side or measure of one angle
Do not need anything else as the triangle can be constructed from the given data

Discuss Question

Answer: Option D. -> Do not need anything else as the triangle can be constructed from the given data
:
D

If the lengths of the two sides enclosing the right angle in a right-angled triangle are given, we do not require any more data to draw the triangle.

Question 75.

Which of the following data is not sufficient to draw a unique triangle?

Side, Side, Angle(not included)
Side, Angle(included), Side
Angle, Angle, Angle
Angle, Angle, Side(not included)

Discuss Question

Answer: Option A. -> Side, Side, Angle(not included)
:
A and C

When all the angles of a triangle are given, then you won't be able to draw a unique triangle. To get a unique triangle at least one side of a triangle should be given.
When two side and included angle is given then, then any unique triangle can be drawn.
Similarily in case of two angles and an included side, a unique triangle can be drawn.

Question 76.

Ram drew $∠ A B C$ and then he drew a line segment $B D$ such that the line segment $B D$ is angle bisector of $∠ A B C$ . Then, $∠ (A B C) =$ __ $\times ∠ (A B D)$ .

Discuss Question

Answer: Option A. -> Side, Side, Angle(not included)
:
As stated in question line segment

B D

is angle bisector so,

∠ A B D = ∠ D B C

And,

∠ A B D + ∠ D B C = ∠ A B C

So,

∠ (A B C) = 2 ∠ (A B D)

Question 77.

Akash tried to make a $Δ A B C$ whose rough figure is given below.

He first drew BC. Then taking B as a centre he drew $7 c m$ arc and C as a centre he drew a $3 c m$ arc.

Will he be able to get the point A? Yes or No.

Discuss Question

Answer: Option A. -> Side, Side, Angle(not included)
:

The sum of any two sides of a triangle is greater than the third side.
Here, $7 c m + 3 c m = 10 c m$ , which is less than $14 c m$ . So, a triangle can't be constructed.
Therefore, Akash will not get the arcs intersecting at any point.

Question 78.

If $∠ A C D =$ $90^{o}$ . Then line segment $A B$ is __ to line segment $C D$ .

Discuss Question

Answer: Option A. -> Side, Side, Angle(not included)
:

When a line segment is perpendicular to another line segment then angle between them is $90^{o}$ .

Question 79.

Pavan drew two lines and he measured some angles. He found that $∠ 1 = ∠ 5$ and so he concluded that the two lines are parallel.

State whether his conclusion is true or false.

True
False
Either length of one side or measure of one angle
Do not need anything else as the triangle can be constructed from the given data

Discuss Question

Answer: Option A. -> True
:
A

If two lines are parallel to each other, then the corresponding angles formed when a transversal passes through them are equal. By the converse of the previous statement, if the corresponding angles are equal, then the lines must be parallel. So, Pavan's conclusion is true.

Question 80.

Kushagra drew two lines, $l$ and $m$ parallel to each other. He drew another line $n$ which is parallel to $m$ . His friend Manish says that the line $n$ will be parallel to line $l$ as well.Manish is correct.