Introduction to Similarity

Q.

Construct any two similar triangles with the ratio of corresponding sides 7:3 and prove that the triangles are similar.

Q.

Find the correct order for constructing an incircle for triangle $△$ABC:

1.Draw a perpendicular from I to any side to a point D.

2.The angular bisectors intersect at the incenter I.

3.Draw the angular bisectors of $\angle$A and $\angle$B.

4.Take ID as the radius and draw a circle.

5.Construct triangle $△$ABC.

1. 1-2-5-4-3

2. 2-3-1-4-5

3. 4-3-5-2-1

4. 5-3-2-1-4

Q.

Given two angles $\angle A=x^{\circ },\angle B=y^{\circ }andAB;(A+B<{90}^{\circ })$, how many triangles can be constructed?

1. One

2. Two

3. Three

4. None of these

Q. The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then

1. $\angle A^{\prime }B{C}^{\prime }\ne \angle CBA$
2. $\angle B{A}^{\prime }{C}^{\prime }=\angle BAC$
3. $\angle CAB=\angle ACB$

Q. Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor $\frac{3}{5}$.

1. 5

Q. Which of the following pair of letters are congruent?

1. A and V
2. p and q
3. E and F
4. c and o

Q. All rectangles are similar.

1. False
2. True

Q.

A line segment AB is divided in the ratio 4:9 by a point C.
Find the length AC (in cm) if AB=26 cm.

1. 8

Q. At least 2 rays need to be constructed to divide a line segment into a given ratio.

1. True
2. False

Q. To divide a line segment, the constructed ray must be at an obtuse angle to the line segment.

1. True
2. False

Q. The faces of regular triangular pyramid are

1. similar
2. neither similar nor congruent
3. congruent
4. data is insufficient

Q.

The number of arcs to be made to divide a line segment in the ratio 5 : 7 using a single ray is ____.

1. 10

2. 12

3. 7

4. 5

Q.

Which of the following are similar?

1. All of the above

2. Circles

3. Squares

4. Equilateral triangles

Q. The faces of a regular triangular pyramid are:

1. congruent
2. similar
3. congruent but not similar
4. similar but not congruent

Q.

Which of the following statements is false?

1. All squares are similar.

2. Similar figures are always congruent.

3. All circles are similar.

4. Congruent figures are always similar.

Q. If the similar triangle constructed is 5/3 times the given one, then 3 parts correspond to the given triangle.

1. True
2. False

Q. Enter the number of points that are to be marked on a ray drawn at an acute angle to one of its sides, to construct a triangle similar to a given triangle with a scale factor $\frac{3}{5}$.

1. 5