Congruent Figures

Q. If the areas of two similar triangles are equal, prove that they are congruent.

Q. Which of the following statement(s) is/are correct for congruent triangles?

1. Congruent triangles have same shape but different size.
2. Congruent triangles have both same shape and same size.
3. Corresponding angles and corresponding sides of congruent triangles are equal.
4. Congruent triangles have same size but different shape.

Q.

Which geometric figures are always similar?

1. Circles and triangles

2. Regular polygons

3. Circles and all regular polygons

4. Circles

Q. Two equilateral triangles are always congruent.

1. True
2. False

Q.

In the given figure, DE || BC and AD : DB = 5 : 4, then $\frac{areaof\Delta DOE}{areaof\Delta DCE}$ is

1. 15 : 4

2. 25 : 16

3. 5 : 14

4. 25 : 196

Q. Fill in the blanks using the correct word given in brackets :

(i) All circles are ......... (congruent, similar).
(ii) All squares are ........(similar, congruent).
(iii) All .......... triangles are similar (isosceles, equilateral):
(iv) Two triangles are similar, if their corresponding angles are .......... (proportional, equal)
(v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ...........(equal, proportional).

Q.

In $△$ABC, the medians BE and CF intersect at G. AGD is a line meeting BC in D. If GD is 1.5 cm, then AD is equal to -

1. 4.5 cm

2. 2.5 cm

3. 3 cm

4. 4 cm

Q. Question 7
Which of the following figures satisfy the following property?
-Has two pairs of congruent adjacent sides.

Q.

If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

1. True
2. False

Q.

1. Figure 1

2. Figure 2

3. Figure 4

4. Figure 3

Q. In the given figure, $\Delta ABC$ and $\Delta AMP$ are right-angled at B and M respectively. [3 MARKS]
Given AC = 10 cm, AP = 15 cm and PM = 12 cm
i) Prove $\Delta ABC\sim \Delta AMP$
ii) Find AB and BC

Q. If $\Delta \text{XYZ}$ and $\Delta \text{ABC}$ are Similar, then which of the following is true?

1. XY = AB, YZ = BC and ZX = AC
2. Both the triangles overlap
3. $\text{Area of}\Delta \text{ABC}\ne \text{Area of}\Delta \text{XYZ}$
4. $\text{Area of}\Delta \text{ABC}=\text{Area of}\Delta \text{XYZ}$

Q.

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

1. ABC

2. AEF

3. BFD, CDE

4. AFE, BFD, CDE

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
(v) Two triangles are similar if their corresponding angles are proportional.
(v) Two triangles are similar if their corresponding angles are equal.

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 proportional.
(iv) Two polygons are similar, if their corresponding angles are proportional.
(v) Two triangles are similar if their corresponding sides are proportional.
(vi) Two triangles are similar if their corresponding angles are proportional.

Q.

Two triangles are congruent if their sides have the same ________ and _____________

Q. Fill in the blanks using the correct word given in brackets :
(i) All circles are _______. (congruent, similar)
(ii) All squares are ________. (similar, congruent)
(iii) All _______ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are _______ and (b) their corresponding sides are ______. (equal, proportional)

Q. In the given figure, ∠AMN = ∠MBC = 76⁰ If p, q and r are the lengths of AM, MB and BC respectively, then express the length of MN in terms of p, q and r.

Q. Question 4
If the areas of two similar triangles are equal, prove that they are congruent.

Q. Factors of x square _4abxsquare _(a square_b square)square?

Q.

Choose the correct alternative :

Which of the following figures are not always congruent?

1. two circles of same radius

2. two squares of same side

3. two line segments of same length

4. two equilateral $△s$

Q. Two equilateral triangles are always congruent.

1. True
2. False

Q.

In the given figure, DE || BC and AD : DB = 5 : 4, then $\frac{areaof\Delta DOE}{areaof\Delta DCE}$ is

1. ABC

2. BFD, CDE

3. AFE, BFD, CDE

4. AEF

Q.

If $\Delta \text{XYZ}$ and $\Delta \text{ABC}$ are congruent, then which of the following is true?

1. $XY=AB,YZ=BC$ and $ZX=AC$

2. Area($\Delta \text{ABC})$ $=$ Area($\Delta \text{XYZ})$

3. Both the triangles can overlap

4. All of these

Q.

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

1. ABC

2. AEF

3. BFD

4. CDE

Q.

In $△$ABC, the medians BE and CF intersect at G. AG is a line when extended meets BC in D. If GD is 1.5 cm, then AD is equal to

1. 2.5 cm

2. 3 cm

3. 4 cm

4. 4.5 cm

Q. Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. The ratio of their corresponding heights is ____.

1. 16:25
2. 25:16
3. 4:5
4. 5:4

Q. If two triangles are , then they are .

1. similar
2. congruent
3. unequal
4. dissimilar

Q. The faces of a regular triangular pyramid are _____.

1. Congruent but not similar
2. Similar but not congruent
3. Neither similar nor congruent
4. Congruent and similar

Q.

Congruent polygons have the same area.

1. True

2. False