Chapter 8: Similar Triangles
1. If ∆ ABC ~ ∆ PQR; ∠A = 320, ∠R = 650, then ∠B =
If ∆ ABC ~ ∆ PQR; ∠A = 320, ∠R = 650, అయిన ∠B =
(1) 930 (2) 830 (3) 730 (4) 630
Answer: (2)
Given ∆ ABC ~ ∆ PQR ⟹ ∠A =∠P; ∠B =∠Q; ∠C =∠R
⟹ ∠C =∠R = 650
Now in ∆ ABC, ∠A + ∠B + ∠C = 1800
320 + ∠B + 650 = 1800
970 + ∠B = 1800
∠B = 1800 – 970 = 830
2. In the ∆ ABC; D, E and F are midpoints of the side BC, CA and AB.T
hen area of ∆ DEF : ∆ ABC = __________
∆ ABC లో D, E మరియు F లు వరుసగా BC, CA మరియు AB ల మధ్య బిన్డువులైన,
∆ DEF వైశాల్యం : ∆ ABC వైశాల్యం = __________
(1) 1 : 4 (2) 4 : 1 (3) 1 : 3 (4) 3 : 4
Answer: (1)
By using mid theorem i.e., the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
∴ DF || BC and DF = 1/2 BC ⟹ DF = BE
Since, the opposite sides of the quadrilateral are parallel and equal.
Hence, BDFE is a parallelogram
Similarly, DFCE is a parallelogram.
Now, in ∆ABC and ∆EFD; ∠ABC= ∠EFD, ∠BCA = ∠EDF
By AA similarity criterion, ∆ABC ~ ∆EFD
If two triangles are similar, then the ratio of their areas is equal to the squares of their corresponding sides
Hence, the ratio of the areas of ∆DEF and ∆ABC is 1 : 4.
TS Polycet
3. In the given figure ∠BAC = 900, AD ⊥ BC, BD = 9 cm and CD = 16 cm then AC =?
ఇచ్చిన పటం నుండి ∠BAC = 900, AD ⊥ BC , BD = 9 cm మరియు CD = 16 cm అయిన AC = ?
(1) 10 cm (2) 15 cm (3) 20 cm (4) 25 cm
Answer: (3)
Given that,
In ΔABC, D is any point on BC such that AD ⊥ BC
We know that AD² = BD × DC
Now, it is given that BD = 12 cm and DC = 16 cm
⟹ AD² = 9 × 16 ⟹ AD² = 144 ⟹ AD = 12 cm
In ΔADC,AC² = AD² + DC²
Now, given that, DC = 16 cm and AD = 12 cm
So, on substituting the values, we get
⟹ AC² = 12² + 16² ⟹ AC² = 144 + 256 ⟹ AC² = 400 ⟹ AC² = 20²
⟹ AC = 20 cm
4. The base of two similar triangles are 24 cm and 18 cm. If one side of first triangle is 8 cm,
then the corresponding side of another triangle is _______
రెండు సరూప త్రిభుజాల పొడవులు 24 cm మరియు 18 cm. ఒక త్రిభుజ భుజం 8 cm అయిన, రెండవ
అనురూప త్రిభుజ భుజం
(1) 8 cm (2) 6 cm (3) 4 cm (4) 2 cm
Answer: (2)
If two triangles are similar, then their corresponding sides are in proportional
⟹ 
⟹ 24x = 18 × 8 ⟹ x = 6
∴ the side of another triangle is 6 cm
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⟹ 24x = 18 × 8 ⟹ x = 6
