Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles. From the information shown in the figure, in ΔABC and ΔPQR &ang;ABC &cong; &ang;PQR seg BC &cong; seg QR &ang;ABC = &ang;PRQ &there4; ΔABC &cong; ΔPQR ……………………____ test &there4; &ang;BAC = _____……………………corresponding angles of congruent triangles. seg AB &cong; ____………………….. corresponding sides of congruent triangles. ____ = seg PR …………………corresponding side of congruent triangles.

Given: ∠ ABC = ∠ PQR BC = QR ∠ ABC = ∠ PRQ ∴ ΔABC ≅ ΔPQR … … ASA test ASA : angle side angle ∴ ∠ BAC = ∠ QPR … . Corresponding angles of congruent triangles seg AB = seg PQ … . Corresponding sides of congruent triangles seg AC = seg PR … . Corresponding sides of congruent triangles

In Δ D E F and Δ P Q R , D E = D F , ∠ F = ∠ P and ∠ E = ∠ Q . The two triangles are

Isosceles but not necessarily congruent

Neither congruent nor isosceles

EASY

Earn 100

Two circles are always congruent.

74.76% studentsanswered this correctly

Important Questions on Triangles

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

In a circle with centre

O, A B

is the diameter and

C D

is a chord such that

A B C D

is a trapezium. If

∠ B A C = 40 °

, then

∠ C A D

is equal to:

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

In a triangle

A B C,

the median

A D

(with

D

B C

) and the angle bisector

B E

(with

E

A C

) are perpendicular to each other. If

A D = 7

and

B E = 9,

find the integer nearest to the area of triangle

A B C .

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

Let

P Q R

be an acute-angled triangle in which

P Q < Q R

. From the vertex

Q

draw the altitude

Q Q_{1}

the angle bisector

Q Q_{2}

and the median

Q Q_{3}

, with

Q_{1,} Q_{2,} Q_{3}

lying on

P R

. Then,

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

Let P be an interior point of a convex quadrilateral

A B C D

and

K, L, M, N

be the mid-points of

A B, B C

respectively. If Area

(P K A N) = 25,

Area

(P L B K) = 36,

and Area

(P M D N) = 41

then Area

(P L C M)

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

In the parallelogram

A B C D

M

and

N

are respectively the midpoints of

A B

and

A D

. The points

M

and

N

are joined to form the triangle

A M N

. The area of the triangle

A M N

and the area of the parallelogram

A B C D

are in the ratio:

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

The area of an equilateral triangle is

49 \sqrt{3} c m^{2}

. Find its side (in

c m

.).

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

Let

A B C

be an acute-angled triangle and

P

be a point in its interior. Let

P_{A}, P_{B}

and

P_{C}

be the images of

P

under reflection in the sides

B C, C A,

and

A B,

respectively. If

P

is the orthocentre of the triangle

P_{A} P_{B} P_{C}

and if the largest angle of the triangle that can be formed by the line segments

P A, P B,

and

P C

x °,

determine the value of

x .

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

In the figure, in $△ A B C, A B = A C = 10 cm and B C = 12 cm .$ $P and Q$ are the midpoints of $A B and A C$ respectively. $P M and R N$ are perpendiculars on $S Q$ . If $B S : S R : R C = 1 : 2 : 1$ , then the length of $M N$ is:

Question Image

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

Let

a = B C, b = C A, c = A B

be the side lengths of a triangle

A B C,

and

m

be the length of the median through

A .

a = 8, b - c = 2, m = 6

, then the nearest integer to

b

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

Let

A B C

be an acute angled triangle with

A B = 15

and

B C = 8 .

Let

D

be a point on

A B

such that

B D = B C .

Consider points

E

A C

such that

∠ D E B = ∠ B E C .

α

denotes the product of all possible values of

A E,

find

\frac{[α]}{10}

, where

[α]

is the integer part of

α .

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

If the diagonal of a quadrilateral bisect each other at right angles, then it is a

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

In the given figure ,if

a r (∆ A B C) = 28 {cm}^{2}

,then

a r (A E D F) =

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

In the given figure, $ABCD$ is a square and $P$ is a point inside it such that $PB = PD$ . Prove that $CPA$ is a straight line.

Question Image

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

Question Image

From the information shown in the figure, in ΔABC and ΔPQR

∠ABC ≅ ∠PQR

seg BC ≅ seg QR

∠ABC = ∠PRQ

∴ ΔABC ≅ ΔPQR ……………………____ test

∴ ∠BAC = _____……………………corresponding angles of congruent triangles.

seg AB ≅ ____………………….. corresponding sides of congruent triangles.

____ = seg PR …………………corresponding side of congruent triangles.

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

Δ D E F

and

Δ P Q R

D E = D F, ∠ F = ∠ P

and

∠ E = ∠ Q

. The two triangles are

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

△ A B C

and

△ D E F

, it is given that

A B = D E

and

B C = E F

. In order that

△ A B C ≅ △ D E F

, we must have

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

Δ A B C, ∠ A = 85^{\circ}, ∠ B = 30^{\circ}

and

∠ C = 65^{\circ}

, then

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

In the given figure, if

P A = P D

and

P B = P C

. Then

Δ P A B

is congruent to _____
Question Image

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

Two right triangles are congruent if any two sides of one are equal to two corresponding sides.

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

△ A B C ≅ △ P Q R

, then which of the following is not true?

Two circles are always congruent.

Important Questions on Triangles

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