# Free Practical Geometry 01 Practice Test - 7th grade

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

A.

Corresponding angles are equal.

B.

Alternate interior angles are equal.

C.

Vertically opposite angles are equal.

D.

Complementary angles are equal.

#### SOLUTION

Solution : 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.

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.

A.

Both the statements are correct.

B.

Statement 1 is correct but statement 2 is incorrect.

C.

Statement 2 is correct but statement 1 is incorrect.

D.

Both the statements are incorrect.

#### SOLUTION

Solution : 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.

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

A.

Side, Side, Angle(not included)

B.

Side, Angle(included), Side

C.

Angle, Angle, Angle

D.

Angle, Angle, Side(not included)

#### SOLUTION

Solution : 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.

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?

A.

Length of the third side

B.

Measure of one angle

C.

Either length of one side or measure of one angle

D.

Do not need anything else as the triangle can be constructed from the given data

#### SOLUTION

Solution : 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.

Ram drew ABC and then he drew a line segment BD such that the line segment BD is angle bisector of ABC. Then, (ABC)= __ ×(ABD).

#### SOLUTION

Solution : As stated in question line segment BD is angle bisector so, ABD=DBC

And, ABD+DBC=ABC

So,(ABC)=2(ABD)

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

__

#### SOLUTION

Solution :

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.

If ACD= 90o. Then line segment AB is __ to line segment CD. #### SOLUTION

Solution :

When a line segment is perpendicular to another line segment then angle between them is 90o.

Akash tried to make a ΔABC whose rough figure is given below. He first drew BC. Then taking B as a centre he drew 7cm arc and C as a centre he drew a 3cm arc.

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

__

#### SOLUTION

Solution :

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

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.

A.

True

B.

False

#### SOLUTION

Solution : A

If two lines are parallel then a line drawn parallel to the one of them will be parallel to the other line too. 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.

A.

True

B.

False

#### SOLUTION

Solution : 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.