Ratio, Similarity and Symmetry Exercises 14.2

Today our topic of discussion is Ratio, Similarity and Symmetry Exercises 14.2.

Ratio, Similarity and Symmetry Exercises 14.2

 

 

Exercise 14.2

1. In triangle ABC if the line DE parallel to BC intersects AB and AC at D and E respectively, then-

(i) ΔABC and ΔADE are similar.

(ii) (AD)/(BD) = (CE)/(AE)

(iii) ΔABC ΔADE = (B * C²)/(D * E²)

Which one of the following is true?

1) i and ii

2) i and iii

3) ii and iii

4) i, ii and iii

Use the information from the adjacent figure to answer the questions 2 and 3:

2. What is the ratio of the height and base of ΔABC?

1) 1/2

2) 4/5

3) 2/5

4) 5/4

3. What is the area of ΔABD in square units?

1) 6

2) 20

3) 40

4) 50

4. If in AABC, PQ ||BC then which one of the following is true?

1) AP / P * B = AQ / Q * C

2) AB / P * Q = AC / P * Q

3) AB AC PQ: BC

4) PQ / B * C = BP / B * Q

 

 

5. Prove that if each of the two triangles is similar to a third triangle, they are congruent to each other.
6. Prove that, if one acute angle of a right-angled triangle is equal to an acute angle of another right-angled triangle, the triangles are similar.
7. Prove that the two right-angled triangles formed by the perpendicular from the vertex containing the right angle are similar to each other and also to the original triangle.
8. In the adjacent figure, ∠B = ∠D and CD = 4AB. Prove that, BD = 5BL

9. A line segment drawn through the vertex A of the parallelogram ABCD intersects the BC and DC at M and N respectively. Prove that BMDN is a constant.
10. In the adjacent figure BD ⊥ AC and DQ = BQ = 2AQ = 1/2 * QC Prove that, DA perp 
11. In the triangles triangle ABC and triangle DEF , ∠A= ∠D. Prove that, triangle ABC : ADEF AB AC: DE DF
12. The bisector AD of LA of the triangle ABC intersects BC at D. The line segment CE parallel to DA intersects the line segment BA extended at E.

1) Draw the figure according to the information.

2) Prove that, BD / D * C = BA / A * C

3) If a line segment parallel to BC intersect AB and AC at P and Q respectively, prove that BD / D * C = BP / C * Q

 

 

13. In the figure, ABC and DEF are two similar triangles.

1) Name the matching sides and matching angles of the triangles.

2) Prove that, triangle ABC triangle DEF = (A * B²)/(D * E ^ 2) = (A * C²)/(D * F²) = (B * C²)/(E * F²)

3) If BC = 3cm , EF = 8cm, ∠B = 60 °. (BC)/(AB) = 3/2 and area of ΔABC is 3 square c m, then draw the triangle triangle hat DEF and find its area.

See more:

• Solution of simple simultaneous equations
• Newtonian Mechanics