# Congruent Figures

## Trending Questions

**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?

- Congruent triangles have same shape but different size.
- Congruent triangles have both same shape and same size.
- Corresponding angles and corresponding sides of congruent triangles are equal.
- Congruent triangles have same size but different shape.

**Q.**

Which geometric figures are always similar?

Circles and triangles

Regular polygons

Circles and all regular polygons

Circles

**Q.**Two equilateral triangles are always congruent.

- True
- False

**Q.**

In the given figure, DE || BC and AD : DB = 5 : 4, then area of ΔDOEarea of ΔDCE is

15 : 4

25 : 16

5 : 14

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 -

4.5 cm

2.5 cm

3 cm

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.

- True
- False

**Q.**

Figure 1

Figure 2

Figure 4

Figure 3

**Q.**In the given figure, ΔABC and ΔAMP are right-angled at B and M respectively. [3 MARKS]

Given AC = 10 cm, AP = 15 cm and PM = 12 cm

i) Prove ΔABC∼ΔAMP

ii) Find AB and BC

**Q.**If ΔXYZ and ΔABC are Similar, then which of the following is true?

- XY = AB, YZ = BC and ZX = AC
- Both the triangles overlap
- Area of ΔABC≠Area of ΔXYZ
- Area of ΔABC=Area of ΔXYZ

**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 –

ABC

AEF

BFD, CDE

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 = 76

^{0}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?

two circles of same radius

two squares of same side

two line segments of same length

two equilateral $\u25b3s$

**Q.**Two equilateral triangles are always congruent.

- True
- False

**Q.**

In the given figure, DE || BC and AD : DB = 5 : 4, then area of ΔDOEarea of ΔDCE is

ABC

BFD, CDE

AFE, BFD, CDE

AEF

**Q.**

If ΔXYZ and ΔABC are congruent, then which of the following is true?

XY=AB, YZ=BC and ZX=AC

Area(ΔABC) = Area(ΔXYZ)

Both the triangles can overlap

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 –

ABC

AEF

BFD

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

2.5 cm

3 cm

4 cm

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 ____.

- 16:25
- 25:16
- 4:5
- 5:4

**Q.**If two triangles are

- similar
- congruent
- unequal
- dissimilar

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

- Congruent but not similar
- Similar but not congruent
- Neither similar nor congruent
- Congruent and similar

**Q.**

Congruent polygons have the same area.

True

False