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Practice each question, then open the answer or worked solution.
In Fig. 2.15, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then
(a) AD = AB + ______
(b) AD = AC + ______
(c) midpoint of AE is ______
(d) midpoint of CE is ______
(e) AE = ______ × AB.
Solution:-
(a) AD = AB + BD
Where, BD = BC + CD
(b) AD = AC + CD
(c) midpoint of AE is c
(d) midpoint of CE is D
(e) AE = 4 × AB. [given]
In Fig. 2.16,
(a) ∠AOD is a/an ______ angle
(b) ∠COA is a/an ______ angle
(c) ∠AOE is a/an ______ angle
Solution:-
From the figure,
(a) ∠AOD is a/an right angle.
Is anyone angle in the triangle is equal to 90o, then the triangle is called a right triangle.
∠AOD = ∠AOB + ∠BOC + ∠COD
= 30o + 20o + 40o
= 90o
(b) ∠COA is a/an acute angle
An acute angle is an angle formed between 0o to 90o.
∠COA = ∠COB + ∠BOA
= 20O + 30O
= 50o
(c) ∠AOE is a/an obtuse angle
An obtuse angle is an angle formed between 90o to 180o.
∠AOE = ∠EOD + ∠DOC + ∠COB + ∠BOA
= 40o + 40o + 20O + 30O
= 130o
The number of triangles in Fig. 2.17 is ______. Their names are ______________________.
Solution:-
The number of triangles in Fig. 2.17 is 5. Their names are ΔAOC, ΔCOD, ΔAOB, ΔACB, ΔACD.
Number of angles less than 180° in Fig. 2.17 is ______and their names are .
Solution:-
The number of angles less than 180° in Fig. 2.17 is 12, and their names are ∠OAB, ∠OBA, ∠OAC, ∠OCA, ∠OCD, ∠ODC, ∠AOB, ∠AOC, ∠COD, ∠DOB, ∠BAC, ∠and ACD.
The number of straight angles in Fig. 2.17 is ______.
Solution:-
The number of straight angles in Fig. 2.17 is four.
The angles are, ∠AOD, ∠BOC, ∠COB, ∠and DOA.
The number of right angles in a straight angle is ______, and that in a complete angle is ______.
Solution:-
The number of right angles in a straight angle is two, and that in a complete angle is four.
We know that the angle formed by a straight angle = 180o
and the angle formed by right angle = 90o
So, number of right angles = 180o/90o= 2
We know that complete angle = 360o
So, number of right angles = 360o/90o= 4
The number of common points in the two angles marked in Fig. 2.18 is ______.
Solution:-
The number of common points in the two angles marked in Fig. 2.18 is two.
From the given figure, the common points are P and Q.
The number of common points in the two angles marked in Fig. 2.19 is ______.
Solution:-
The number of common points in the two angles marked in Fig. 2.19 is one.
From the given figure, the common point is A.
The number of common points in the two angles marked in Fig. 2.20 ______.
Solution:-
The number of common points in the two angles marked in Fig. 2.20 three.
From the given figure, the common points are P, Q and R.
The number of common points in the two angles marked in Fig. 2.21 is ______.
Solution:-
The number of common points in the two angles marked in Fig. 2.21 is four.
From the given figure, the common points are D, E, F and G.