Similar Polygons

Q.

Select all the conditionals that have a true converse.

1. If a quadrilateral is a square, then it has four congruent sides.

2. If a polygon is a triangle, then it has $3$ sides.

3. If a quadrilateral is a rectangle, then it has two pairs of parallel sides.

4. If two angles are congruent, then they have the same measure.

5. If two angles are complimentary, then the sum of the measures of the angles is $90$.

Q.

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

Q.

The scale factor (for similar triangles) can be infinity.

1. False

2. True

Q.

If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the two triangles are __________.

1. Both similar and congruent

2. Similar

3. Congruent

4. Neither similar nor congruent

Q.

All circles are ___.

Q. Which of the following statements is false regarding similarity of triangles?

1. If two triangles are similar, their sides are proportional.
2. (b) and (c) above.
3. If two triangles are similar, their sides are equal.
4. If two triangles are similar, their angles are equal.

Q. Question 1 (ii)
Fill in the blanks using the correct word in the given bracket.

(ii) All squares are ____.(similar, congruent)

Q.

Question 1 (i)
Fill in the blanks using the correct word in the given bracket.

(i) All circles are___. (congruent, similar)

Q.

Are the below shown regular hexagons are similar figures?

1. False

2. True

Q.

In both the figures given below, all of the respective sides are equal and all interior angles are ${90}^{\circ }$. The figures shown below are similar.

1. True

2. False

Q.

Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.

1. True
2. False

Q.

Two identical rectangles are to be cut along the diagonals and the triangles got joined with another rectangle, to make a regular hexagon as shown below:

What should be dimensions of the rectangles?

Q.

A point O in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that: ${OA}^2$ + ${OC}^2$ = ${OB}^2$ + ${OD}^2$.

Q. Question 1 (ii)
Fill in the blanks using the correct word in the given bracket.

(ii) All squares are ____.(similar, congruent)

Q.

Which of the following are similar?

1. Circles

2. Squares

3. Equilateral triangles

4. All of the above

Q. Write the truth value (T/F) of each of the following statements.
(i) Any two similar figures are congruent.
(ii) Any two congruent figures are similar.
(iii) Two polygons are similar, if their corresponding sides are porportional
(iv) Two polygons are similar, if their corresponding angles are porportional

Q. Question 1 (ii)
Fill in the blanks using the correct word in the given bracket.

(ii) All squares are ____.(similar, congruent)

Q.

In both the figures given below, all of the respective sides are equal and all interior angles are ${90}^{\circ }$. The figures are similar.

1. False

2. True

Q.

Are the below shown figures similar?

1. True

2. False

Q. Question 1 (i)
Fill in the blanks using the correct word in the given bracket.

(i) All circles are___. (congruent, similar)

Q. State True and False. In triangles of the same angles drawn in different sizes, the lengths of the sides are different, but their ratios are the same.

1. True
2. False

Q.

The given figure shows a trapezium in which AB is parallel to DC and diagonals AC and BD intersect at point P, If AP : CP = 2 : 3.

Find -

(i) $\Delta APB:\Delta CPB$

(ii) $\Delta DPC:\Delta APB$

(iii) $\Delta ADP:\Delta APB$

1. (i) 3 : 2, (ii) 4 : 9, (iii) 3 : 2

2. (i) 2 : 3, (ii) 9 : 4, (iii) 3 : 2

3. (i) 1 : 2, (ii) 3 : 2, (iii) 2 : 3

4. (i) 9 : 4, (ii) 2 : 3, (iii) 5 : 3

Q.

Fill in the blanks using the correct word given in brackets: All circles are _______. (congruent/similar)

Q.

In both the figures given below, all of the respective sides are equal and all interior angles are ${90}^{\circ }$. The figures shown below are similar. State whether true or false.

1. True

2. False

Q.

Question 1 (i)
Fill in the blanks using the correct word in the given bracket.

(i) All circles are___. (congruent, similar)

Q.

$Inthegivenfigure,DE\parallel BC.Then,△ADEisnotsimilarto△ABC$

1. True

2. False

Q.

Are the shown regular hexagons similar figures?

1. True

2. False

Q.

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD ∼ ΔECF

Q.

In both the figures given below, all of the respective sides are equal and all interior angles are ${90}^{\circ }$. The figures shown below are similar. State True/False?

1. True

2. False

Q.

In both the figures given below, all of the respective sides are equal and all interior angles are ${90}^{\circ }$. Are the figures shown below similar?

1. True

2. False