Reducing Triangles and Observing Their Angles

Q. In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.

Q. If two triangles are similar, then which of the following statement(s) is/are correct?

1. Corresponding angles are equal.
2. Ratio of corresponding angles are equal.
3. Corresponding sides are equal.
4. Ratio of corresponding sides are equal.

Q. 57. The side of a right angle triangle is 17 cm less than the other side. If length of hypoteneuse is 25 cm, find the length of Sides

Q.

There are two triangles ABC and XYZ such that ΔABC ΔYXZ. their measurement are given as follows: AB =6 cm, AC = 9 cm, BC = 7 cm. Find out the corresponding measurements of triangle YXZ.

1. XY = 9 cm, YZ = 6 cm, XZ = 7 cm

2. XY = 6 cm, YZ = 9 cm, XZ = 7 cm

3. XY = 9 cm, YZ = 7 cm, XZ = 6 cm

4. XY = 7, YZ = 9 cm, XZ = 6 cm

Q.

In two similar triangles, ABC and DEF AB=4 cm, DE=5 cm.What is the ratio of the perimeters of triangles ABC and DEF?

1. 

2. 

3. 

4. 

Q. The bisector of angle A and angle B of triangle ABC meet at P and PQ, PR are parallel to AC and BC. The perimeter of triangle PQR is 30cm. What is the length of AB.

Q.

State true or false:

When the sides of a triangle are reduced by the same percentage, the measures of angles decrease in the same ratio.

1. True

2. False

Q. In a triangle ABC, angle ABC = 90 and BD is perpendicular to AC. If BD = 8 cm and AD = 4 cm then find the length of CD?

Q.

If the ratio of the perimeters of two similar triangles ABC and DEF is 3:7 .What is the ratio of their corresponding sides?

1. 3:5

2. 1:7

3. 2:3

4. 3:7

Q. Show that the difference of any two sides of a triangle is less than the third side.

Q. If all three sides of a triangle are reduced by 20% without changing the angles, the new and the original triangles will be:

1. Congruent
2. Similar
3. Not similar
4. Equilateral

Q.

All isosceles triangle are similar.

1. True
2. False