# Grade 7 Triangles and Their Congruence Worksheet Questions and Answers (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Tick (✓) if the Given Lengths Can Be of the Three Sides of a Triangle.

(a)

(b)

(c)

(d)

(2) Find the Value of X Using Pythagoras Theorem.

(a)

(b)

(c)

(3) a 1.8 m Long Ladder is Placed Against a Wall in Such a Way That the Roof of the Ladder is 1.2 M Away from the Wall. Find the Height of the Point on the Wall Where the Ladder Rests.

(4) Tick (✓) if the Given Statement is True.

(a) In right angle triangle length of square of hypotenuse is equal to sum of square of two other side.

(b) Equilateral triangle has all the angle of same size of 50 degree.

(5) Only One of the Figures Given on the Right is Congruent to the Figure on the Left. Tick (✓) That Figure.

(6) Find the Value of the Unknown if the Two Triangles Are Congruent.

(a)

(b)

(7) The Two Given Triangles Are Congruent. Write in Their Congruence Relation and the Congruence Criterion.

(a)

(8) The Two Given Triangles Are Congruent. Write in Their Congruence Relation and the Congruence Criterion.

(a)

(9) The Two Given Triangles Are Congruent. Write in Their Congruence Relation and the Congruence Criterion.

(a)

(10) The Two Given Triangles Are Congruent. Write in Their Congruence Relation and the Congruence Criterion.

(a)

(11) if Statement is Right Tick (✓) Otherwise (✗)

(a) Two triangles are congruent if their corresponding sides are equal

(b) The ASA congruence criterion holds true only when the corresponding sides are included sides.

(c) Two equilateral triangles, with the same length of sides, are congruent

(12) In the Given Figure, MN = RQ and NO = QP and Angle N and Angle Q Are Right Angle Than Prove That PM = or

(13) In below Figure TM = TN. M is Midpoint of TR and N is Midpoint of TS. Then Prove That RN = MS

(14) in below Figure AB = CB and BD Bisects Angle B Than Prove That AE = CE.

Given length of three sides of triangle are: 15 cm, 20 cm, and 7 cm

This sides can form a triangle if summation of length of two smaller side is greater than the length of third side.

So, Summation of length of two smaller side is:

So, 22 cm is greater than 20 cm. so this side can form a triangle.

Given length of three sides of triangle are: 5 cm, 8 cm, and 10 cm

This sides can form a triangle if summation of length of two smaller side is greater than the length of third side.

So, Summation of length of two smaller side is:

So, 13 cm is greater than 10 cm. so this side can form a triangle.

Given length of three sides of triangle are: 40 cm, 25 cm, and 70 cm

This sides can form a triangle if summation of length of two smaller side is greater than the length of third side.

So, Summation of length of two smaller side is:

So, 65 cm is less than 70 cm. so this side cannot form a triangle.

Given length of three sides of triangle are: 10 cm, 15 cm, and 20 cm

This sides can form a triangle if summation of length of two smaller side is greater than the length of third side.

So, Summation of length of two smaller side is:

So, 25 cm is greater than 20 cm. so this side can form a triangle.

For given right angle triangle length of hypotenuses is x and length of other side is 4 cm and 7 cm.

As per Pythagoras theorem

Therefore, length of hypotenuses side is 8.06 cm

For given right angle triangle length of hypotenuses is 20 cm and length of other side is x cm and 12 cm.

As per Pythagoras theorem

Therefore, length of side-1 is 16 cm

For given right angle triangle length of hypotenuses is x cm and length of other side is 5 cm and 12 cm.

As per Pythagoras theorem

Therefore, length of hypotenuses side is 13 cm

Given data represent as a picture form as below,

Now from figure can say that this form a right-angle triangle and ladder is hypotenuses of right-angle triangle.

So, as per Pythagoras theorem;

Therefore, the height of the point on the wall where the ladder rests is 1.34 m

Given statement that: In right angle triangle length of square of hypotenuse is equal to sum of square of two other side.

This is Pythagoras theorem statement that length of square of hypotenuse is equal to sum of square of two other side.

So, it՚s right statement

In right angle triangle length of square of hypotenuse is equal to sum of square of two other side.

Given statement that: Equilateral triangle have all the angle of same size of 50 degree.

For equilateral triangle all the angle has same size 60 degree. so given statement is wrong.

Equilateral triangle has all the angle of same size of 50 degree.

Figure is said to be congruent to given figure if both the figure has same length or size.

Here given figure is a line having length 8 cm

Therefore, for congruent to given figure among right side all figure the line having length of 8 cm is congruent to given figure.

Therefore;

Figure is said to be congruent to given figure if both the figure has same length or size.

Here figure is pentagon and congruent figure to the given pentagon is

If given each triangle is congruent than its respective angle and length of side have same value.

Therefore, for angle

And for side

If given each triangle is congruent than its respective angle and length of side have same value.

Therefore, for side-1

And for Side-2

From figure for given two triangles △DAC and △BAC it is given that;

Therefore, as per Congruent triangle rule SSS (if 3 sides in one triangle are congruent to 3 sides of a second triangle, then the triangle are congruent) this two triangle Congruent.

Therefore

From figure for given two triangles △PTQ and △RTS given that;

Angle T for triangle for both the triangle is angle formed by two line.

This angle are vertically opposite angle and vertically opposite angle are always same.

Therefore, Angle T in both triangles have same value

Therefore

Therefore, as per Congruent triangle rule SAS (if 2 sides and included angle of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent) this two triangle Congruent.

Therefore

From figure for given two triangles △LJK and △NOM it is given that;

Therefore, as per Congruent triangle rule SAS (if 2 sides and included angle of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent) this two triangle Congruent.

Therefore

From figure for given two triangles △PTQ and △RSQ it is given that;

Therefore, as per Congruent triangle rule ASA (if 2 Angles and included Side of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent) this two triangle Congruent.

Therefore

Given statement: Two triangles are congruent if their corresponding sides are equal

Two triangles can be congruent by either ASA, SAS, SSS, or AAS means at least there should be three corresponding similarities.

In given triangle there are only two similarities therefore we cannot say that this given two triangles are congruent,

Therefore, two triangles are congruent if their corresponding sides are equal

Given statement: The ASA congruence criterion holds true only when the corresponding sides are included sides.

As per ASA rules: if 2 Angles and included Side of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent

That means it is compulsory that criterion holds true only when the corresponding sides are included sides.

If it՚s not included side that Congruence will change and become AAS.

Therefore; criterion holds true only when the corresponding sides are included sides.

Given statement: Two equilateral triangles, with the same length of sides, are congruent

For two equilateral triangles with same length of side it becomes SSS congruence

So, this two-triangle become congruent to each other as per SSS rule.

Therefore; Two equilateral triangles, with the same length of sides, are congruent

From figure consider two triangles △MNP and △RQO

Now it՚s given that;

And from figure

For triangle △MNP from figure

And for triangle △RQO from figure

Therefore, for two triangle △MNP and △RQO

Therefore, as per Congruent triangle rule SAS (if 2 sides and included angle of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent) this two triangle Congruent.

Therefore

Therefore, we can say that;

For figure given that

And M is midpoint of TR than we can write that

Therefore

Now, given that N is mod point of TS so we can write that

Therefore,

Now for triangle △TNR and △TMS we can write that;

Therefore, as per Congruent triangle rule SAS (if 2 sides and included angle of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent) this two triangles are Congruent.

Therefore

Therefore, we can say that;

For figure given that;

And BD bisects angle B.

From figure BD bisects angle B than we can write that

Now consider two triangles △ABE and △CBE

Therefore, as per Congruent triangle rule SAS (if 2 sides and included angle of one triangle are congruent to the corresponding parts of the other triangle, the triangles are congruent) this two triangles △ABE and △CBE are Congruent.

Therefore,

Therefore, we can say that;

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