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

7th Grade > Mathematics

PRACTICAL GEOMETRY MCQs

Total Questions : 105 | Page 4 of 11 pages

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

:
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 32. Pavan drew two lines and he measured some angles. He found that

∠ 1 = ∠ 5

and so he concluded that the two lines are parallel.

Pavan Drew Two Lines And He Measured Some Angles. He Found T...

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. Bythe converse of the previous statement, if the corresponding angles are equal, then the lines must be parallel. So, Pavan's conclusion is true.

Question 33. 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

iscorrect whilestatement

1

is incorrect.
Reason:-If the lines are perpendicular to each other, then the pair of vertically opposite angles are also supplementary.

Question 34. If line segment

A B

is perpendicular to

C D

then

∠ D C A

= ? (in degrees)

If Line Segment AB Is Perpendicular To CD Then ∠DCA = ? (i...

Discuss Question

:
When a line segment is perpendicular to another line segment then angle between them is

90^{\circ}

Question 35. The lines shown below never meet at any point. So, these lines are not parallel. Say true or false.

True
False
acute-angled
equilateral

Discuss Question

Answer: Option B. -> False
:
B
Parallel lines never intersect. Parallel linesarelinesin a plane which do not meet, that is, twolinesin a plane that do not intersect or touch each other at any point are said to beparallel.

Question 36. Pavan tried to draw a line parallel to a given line, 'l'. Few steps are shown below. What will be the next step?
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.

Draw another arc with the same radius and A as the centre, such that it intersects AB at F
Draw another arc with B as the centre and distance DE as the radius
Draw another arc with some other radius and A as the centre
Draw another arc with B as the centre and distance AB as the radius

Discuss Question

Answer: Option A. -> Draw another arc with the same radius and A as the centre, such that it intersects AB at F
:
A
Following are the steps to draw aline 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 segmentjoining 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 intersectsABat 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.
Line 'm' is the required parallel line.

Question 37. If the sides of a triangle are

3 cm, 4 cm, and 5 cm

. Then, the triangle formed is a/an _____ triangle.

right-angled
obtuse-angled
acute-angled
equilateral

Discuss Question

Answer: Option A. -> right-angled
:
A
Let us construct the required triangle as follows:
Step 1:
Draw the base line XYof the length 3cm.
Step 2:
Use your compass to make an arcwith centre at point Yand the radius 4cm.
Step 3:
Use your compass to make a circle with centre at point Xand the radius 5cm.
Step 4:
The point of intersection between the arcs is named as X.
The triangle is completed by joining all these three points.

If The Sides Of A Triangle Are 3 cm, 4 cm, And 5 cm. Then...

Now, fromabove constructionwe see that the triangle formed is a right angle triangle.

Question 38. Raman had to draw an isosceles triangle with base angles as

65^{\circ}

each and base length of

5 c m

. Raman said the given data is insufficient. Is he correct?

True
False
acute-angled
equilateral

Discuss Question

Answer: Option B. -> False
:
B
We are given two angles and one side. So, data is sufficient and the triangle can be drawn.

Question 39. How many right angles are there in a cubical room? [1 MARK]

Discuss Question

:
Each corner has three mutually perpendicular linesand a cuboid has 8 corners. Hence, the total number of right angles in a cubical room is

8 \times 3 = 24

Question 40. (a) Draw a line l. Draw a perpendicular on l at any point. On this perpendicular, choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.
(b) Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as the centre an arc FG is drawn (as shown in the figure).

What is the relation between the length of arc DM and arc FG?
[4 MARKS]

Discuss Question

:
Each part: 2 Marks
(a) To construct: A line parallel to given line when the perpendicular line is also given.

Draw a line l and take a point P on it.
At point P, draw a perpendicular line n.
Take PX = 4 cm on line n.
At point X, again draw the line m.
(b)Since both the angles are alternate interior angles, they will be equal to each other. Also, since both arcs are drawn with the same radius, they are part of two equal circles. This means that they both have same shape and size. Thus, the two arcs DM and FG are congruent which makestheir lengthsequal.