Question

SIMILARITY OF TRIANGLES:
Teacher gives activity to the students to measure the height of the tree and asks them who will do this activity. Anjali accepts the challenge. She places a mirror on level ground to determine the height of a tree. She stands at a certain distance so that she can see the top of the tree reflected from the mirror. Anjali’s eye level is 1.8 m above the ground. The distance of Anjali and the tree from the mirror are 1.5 m and 2.5 m respectively. Answer the questions below.

i) Name the two similar triangles formed.
a. ∆ ABM ~ ∆ CMD
b. ∆ AMB ~ ∆ CDM
c. ∆ ABM ~ ∆ MDC
d. None of these

ii) State the criteria of similarity that is applicable here.
a. SSS Criterion
b. SAS Criterion
c. AA Criterion
d. ASA Criterion
iii) Find the height of the tree.
a. 3 m
b. 3.5 m
c. 2.5 m
d. 4 m

iv) If ∆ ABM and ∆ CDM are similar, CD = 6 cm, MD = 8 cm and BM = 24 cm. Then findAB.
a. 17 cm
b. 18 cm
c. 12 cm
d. 24 cm

v) In ∆ ABM , if ∠ BAM = 30° then find ∠ MCD
a. 40°
b. 45°
c. 60°
d. 30°

(Provide an explanation as well)
Grade 10

Answer 1

1.a

2.c

3.d

4.b

5.a

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Answer 2

Step-by-step explanation:

SIMILARITY OF TRIANGLES:

Teacher gives activity to the students to measure the height of the tree and asks them who will do this activity. Anjali accepts the challenge. She places a mirror on level ground to determine the height of a tree. She stands at a certain distance so that she can see the top of the tree reflected from the mirror. Anjali’s eye level is 1.8 m above the ground. The distance of Anjali and the tree from the mirror are 1.5 m and 2.5 m respectively. Answer the questions below.

i) Name the two similar triangles formed.

a. ∆ ABM ~ ∆ CMD

b. ∆ AMB ~ ∆ CDM

c. ∆ ABM ~ ∆ MDC

d. None of these

ii) State the criteria of similarity that is applicable here.

a. SSS Criterion

b. SAS Criterion

c. AA Criterion

d. ASA Criterion

iii) Find the height of the tree.

a. 3 m

b. 3.5 m

c. 2.5 m

d. 4 m

iv) If ∆ ABM and ∆ CDM are similar, CD = 6 cm, MD = 8 cm and BM = 24 cm. Then findAB.

a. 17 cm

b. 18 cm

c. 12 cm

d. 24 cm

v) In ∆ ABM , if ∠ BAM = 30° then find ∠ MCD

a. 40°

b. 45°

c. 60°

d. 30°