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09
NCERT Solutions · Maths Ch 9
Geometric Twins
14 questions · 3 exercises
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Ex 9.1
Ex 9.2
Ex 9.3
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 9.1 · 2 QUESTIONS
Geometric Twins
Q1
Check if the two figures are congruent. Circle the pairs that appear congruent (pictures on page 3).
(2 marks)
Q2
What measurements would you take to create a figure congruent to a given: (a) Circle (b) Rectangle
(2 marks)
2
EXERCISE 9.2 · 6 QUESTIONS
Congruence of Triangles
Q3
Suppose ΔHEN is congruent to ΔBIG. List all the other correct ways of expressing this congruence.
(2 marks)
Q4
Determine whether the triangles are congruent. If yes, express the congruence. (ΔRED has RE = 3.5 cm, ED = 5 cm, RD = 6 cm; ΔJAM has JA = 3.5 cm, AM = 5 cm, JM = 6 cm.)
(3 marks)
Q5
Identify whether the triangles are congruent. What conditions did you use? Express the congruence. (ΔABC has AB = 7 cm, BC = 5 cm, ∠B = 47°; ΔXYZ has XZ = 7 cm, YZ = 5 cm, ∠Z = 47°.)
(3 marks)
Q6
Given that CD and AB are parallel and AB = CD, with AD and BC intersecting at O, what are the other equal parts in this figure? Are the two resulting triangles congruent? If so, express the congruence.
(3 marks)
Q7
Given that ∠ABC = ∠DBC and ∠ACB = ∠DCB, show that ∠BAC = ∠BDC. Are the two triangles congruent?
(3 marks)
Q8
Identify the equal parts in the figure (A, D at the top; B, C at the bottom; AC and BD cross at O), given that ∠ABD = ∠DCA and ∠ACB = ∠DBC.
(3 marks)
3
6 QUESTIONS
Exercise 9.3
Q9
ΔAIR ≅ ΔFLY. Identify the corresponding vertices, sides and angles.
(2 marks)
Q10
Each case contains measurements from two triangles ABC and DEF. Identify the pairs in which the triangles are congruent, with reason, and express the congruence. (a) AB = DE, BC = EF, CA = DF (b) AB = EF, ∠A = ∠E, AC = ED (c) AB = DF, ∠B = ∠D = 90°, AC = FE (d) ∠A = ∠D, ∠B = ∠E, AC = DF (e) AB = DF, ∠B = ∠F, AC = DE
(5 marks)
Q11
It is given that OB = OC and OA = OD. Show that AB is parallel to CD. [Hint: AD is a transversal for these two lines. Are there any equal alternate angles?]
(3 marks)
Q12
ABCD is a square. Show that ΔABC ≅ ΔADC. Is ΔABC also congruent to ΔCDA? Give more examples of two triangles where one is congruent to the other in two different ways. Can you give an example of two triangles where one is congruent to the other in six different ways?
(3 marks)
Q13
Find ∠B and ∠C if A is the centre of the circle (∠BAC = 120°).
(3 marks)
Q14
Find the missing angles in the figure on page 21 (a rectangle ABDC-type figure divided into many triangles; equal segments are marked with ticks).
(3 marks)