# Free Practical Geometry 03 Practice Test - 7th grade

Statement 1: It is possible to construct a unique triangle when the measurements of two sides and non-included angle are given.

Statement 2: It is possible to construct a triangle when the measurements of two sides and included angle are given.

Choose the correct option.

A. Both the statements are false
B. Statement 1 is right and Statement 2 is wrong
C. Statement 2 is right and Statement 1 is wrong
D. Both the statements are correct

#### SOLUTION

Solution : C

It is possible to construct a triangle when the measurements of two sides and included angle are given. (SAS rule of construction)

If ACD=90 and CF is the angular bisector of ACD, then BCF= __. #### SOLUTION

Solution : Given, ACD = 90 and CF is the angular bisector of ACD, so DCF=45. So, BCF=135.

In the given figure, AB||CD and if CFE=90, then FEB= __. #### SOLUTION

Solution :

As stated in question AB||CD and if CFE = 90, so FEB is an alternate angle to CFE which should be equal.
So, CFE=90.

Akash was given lengths of two sides and the measure of an angle which is not included between the two sides. But still he was able to draw the triangle. So what should be the angle that was given? (in degrees)

__

#### SOLUTION

Solution :

If he was able to draw a triangle with two sides and an angle which is not included, then the triangle should be a right angled triangle.

The minimum number of triangles that can be drawn if two sides and one angle has been given is __.

#### SOLUTION

Solution :

The minimum number of triangles that can be drawn if two sides and one angle has been given is 0 since the angle might not be an included one.

Preeti is trying to draw a line parallel to PQ through a point R (not on PQ). How many arcs will she need to draw and how many times she needs to change the distance between the compass tip and the pencil tip respectively?

A.

1 and 2

B.

2 and 1

C.

3 and 1

D.

0 and 2

#### SOLUTION

Solution : C

Steps for drawing a line parallel to a given line:

Step 1: Mark a point A, not on the line 'l'.
Step 2: Mark point B on line 'l'.
Step 3: Draw line segment joining points A and B.
Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.
Step 5: Draw another arc with the same radius and A as the centre, such that it intersects AB at F.
Step 6: Draw another arc with F as the centre and distance DE as the radius.
Step 7: Mark the point of intersections of this arc and the previous arc as G.
Step 8: Draw line 'm' passing through points A and G.

No. of arcs drawn = 3
No. of times the distance between compass tip and pencip tip is changed = 1

Preeti told Pavani that if the alternate interior angles are equal then lines need not be parallel. Is Preeti's statement true or false?

A.

True

B.

False

#### SOLUTION

Solution : B

If two parallel lines are intersected by a transversal: (i) alternate interior angles are equal i.e., 2=8 and 3=5

(ii) alternate exterior angles are equal i.e., 1=7 and 4=6

(iii) corresponding angles are equal i.e., 1=5,4=8,2=6 and 3=7

(iv) co-interior angles are supplementary i.e., 2 +5= 180and 3 +8 =180.

Hence, if the alternate angles are equal then the lines are parallel.

Harman told Kushagra that only one line parallel to a given line can be drawn through a point which is not on the line. State whether Harman's statement is true or false.

A.

True

B.

False

#### SOLUTION

Solution : A

We can only draw one line parallel to a given line passing through a point that is not on the line.

Kushagra is drawing a railway track on paper as a part of his project. He asked Sarosh to draw a line parallel to the given line. Sarosh said that we can only construct a line parallel to the given line using alternate angles concept. Is this true?

A.

True

B.

False

#### SOLUTION

Solution : B

We can construct a line parallel to a given line by using alternate angles as well as corresponding angles concept. So, the statement is false.

If two parallel lines are intersected by a transversal: (i) alternate interior angles are equal i.e., 2=8 and 3=5

(ii) alternate exterior angles are equal i.e., 1=7 and 4=6

(iii) corresponding angles are equal i.e., 1=5,4=8,2=6 and 3=7

(iv) co-interior angles are supplementary i.e., 2+5=180 and 3+8=180

A line can be constructed parallel to a given line by making any of the above mentioned pairs of angles equal.

Goutham has been asked to draw a triangle with three lengths given to him. He hasn't checked the given lengths and promised that he will draw the triangle thinking that a triangle can always be constructed with any three lengths. Is it true that a triangle can always be constructed with any three lengths?

A.

True

B.

False

#### SOLUTION

Solution : B

The triangle inequality states that for any triangle, the sum of the lengths of any two of its sides must be greater than the length of the third side. ​We, thus, cannot construct a triangle with any three lengths.