#### Chapters

## Chapter 4: Geometry

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 2 Answers Guide Chapter 4 GeometryExercise 4.1 [Pages 73 - 75]

Can 30°, 60° and 90° be the angles of a triangle?

Can you draw a triangle with 25°, 65° and 80° as angles?

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

Two line segments `bar("AD")` and `bar("BC")` intersect at O. Joining `bar("AB")` and `bar("DC")` we get two triangles, ∆AOB and ∆DOC as shown in the figure. Find the ∠A and ∠B

Observe the figure and find the value of ∠A + ∠N + ∠G + ∠L + ∠E + ∠S

If the three angles of a triangle are in the ratio 3 : 5 : 4, then find them

In ∆RST, ∠S is 10° greater than ∠R and ∠T is 5° less than ∠S, find the three angles of the triangle

In ∆ABC, if ∠B is 3 times ∠A and ∠C is 2 times ∠A, then find the angle

In ∆XYZ, if ∠X : ∠Z is 5 : 4 and ∠Y = 72°. Find ∠X and ∠Z

In a right angled triangle ABC, ∠B is right angle, ∠A is x + 1 and ∠C is 2x + 5. Find ∠A and ∠C

In a right angled triangle MNO, ∠N = 90°, MO is extended to P. If ∠NOP = 128°, find the other two angles of ∆MNO

Find the value of x in the given triangle

Find the value of x in the given triangle

In ∆LMN, MN is extended to O. If ∠MLN = 100 – x, ∠LMN = 2x and ∠LNO = 6x – 5, find the value of x

Using the given figure find the value of x.

Using the diagram find the value of x.

#### Objective type questions

The angles of a triangle are in the ratio 2 : 3 : 4. Then the angles are

20, 30, 40

40, 60, 80

80, 20, 80

10, 15, 20

One of the angles of a triangle is 65°. If the difference of the other two angles is 45°, then the two angles are

85°, 40°

70°, 25°

80°, 35°

80°, 135°

In the given figure, AB is parallel to CD. Then the value of b is

112°

68°

102°

62°

In the given figure, which of the following statement is true?

x + y + z = 180°

x + y + z = a + b + c

x + y + z = 2(a + b + c)

x + y + z = 3(a + b + c)

An exterior angle of a triangle is 70° and two interior opposite angles are equal. Then measure of each of these angle will be

110°

120°

35°

60°

In a ∆ABC, AB = AC. The value of x is ________

80°

100°

130°

120°

If an exterior angle of a triangle is 115° and one of the interior opposite angles is 35°, then the other two angles of the triangle are

45°, 60°

65°, 80°

65°, 70°

115°, 60°

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 2 Answers Guide Chapter 4 GeometryExercise 4.2 [Pages 83 - 86]

Given that ∆ABC ≅ ∆DEF List all the corresponding congruent sides

Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles

If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles

If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles

If the given triangles ΔABC and ΔEFG are congruent, determine whether the given pair of sides and angles are corresponding sides or corresponding angles or not

∠A and ∠G

If the given triangles ΔABC and ΔEFG are congruent, determine whether the given pair of sides and angles are corresponding sides or corresponding angles or not

∠B and ∠E

If the given triangles ΔABC and ΔEFG are congruent, determine whether the given pair of sides and angles are corresponding sides or corresponding angles or not

∠B and ∠G

`bar("AC")` and `bar("GF")`

`bar("BA")` and `bar("FG")`

`bar("EF")` and `bar("BC")`

State whether the two triangles are congruent or not. Justify your answer

State whether the two triangles are congruent or not. Justify your answer

State whether the two triangles are congruent or not. Justify your answer

State whether the two triangles are congruent or not. Justify your answer

State whether the two triangles are congruent or not. Justify your answer

To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion

To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion

To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion

For the given pair of triangles state the criterion that can be used to determine the congruency?

For the given pair of triangles state the criterion that can be used to determine the congruency?

For the given pair of triangles state the criterion that can be used to determine the congruency?

For the given pair of triangles state the criterion that can be used to determine the congruency?

For the given pair of triangles state the criterion that can be used to determine the congruency?

For the given pair of triangles state the criterion that can be used to determine the congruency?

Construct a triangle XYZ with the given conditions.

XY = 6.4 cm, ZY = 7.7 cm and XZ = 5 cm

Construct a triangle XYZ with the given conditions.

An equilateral triangle of side 7.5 cm

Construct a triangle XYZ with the given conditions.

An isosceles triangle with equal sides 4.6 cm and third side 6.5 cm

Construct a triangle ABC with given conditions.

AB = 7 cm, AC = 6.5 cm and ∠A = 120°

Construct a triangle XYZ with the given conditions.

BC = 8 cm, AC = 6 cm and ∠C = 40°

Construct a triangle XYZ with the given conditions.

An isosceles obtuse triangle with equal sides 5 cm

Construct a triangle PQR with given conditions.

∠P = 60°, ∠R = 35° and PR = 7.8 cm

Construct a triangle PQR with given conditions.

∠P = 115°, ∠Q = 40° and PQ = 6 cm

Construct a triangle PQR with given conditions.

∠Q = 90°, ∠R = 42° and QR = 5.5 cm

#### Objective type questions

If two plane figures are congruent then they have

same size

same shape

same angle

same shape and same size

Which of the following methods are used to check the congruence of plane figures?

translation method

superposition method

substitution method

transposition method

Which of the following rule is not sufficient to verify the congruency of two triangles

SSS rule

SAS rule

SSA rule

ASA rule

Two students drew a line segment each. What is the condition for them to be congruent?

They should be drawn with a scale

They should be drawn on the same sheet of paper

They should have different lengths

They should have the same length

In the given figure, AD = CD and AB = CB. Identify the other three pairs that are equal

∠ADB = ∠CDB, ∠ABD = ∠CBD, BD = BD

AD = AB, DC = CB, BD = BD

AB = CD, AD = BC, BD = BD

∠ADB = ∠CDB, ∠ABD = ∠CBD, ∠DAB = ∠DBC

In ∆ABC and ∆PQR, ∠A = 50° = ∠P, PQ = AB, and PR = AC. By which property ∆ABC and ∆PQR are congruent?

SSS property

SAS property

ASA property

RHS property

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 2 Answers Guide Chapter 4 GeometryExercise 4.3 [Pages 86 - 87]

#### Miscellaneous Practice problems

In an isosceles triangle one angle is 76°. If the other two angles are equal find them

If two angles of a triangle are 46° each, how can you classify the triangle?

If an angle of a triangle is equal to the sum of the other two angles, find the type of the triangle

If the exterior angle of a triangle is 140° and its interior opposite angles are equal, find all the interior angles of the triangle

In ∆JKL, if ∠J = 60° and ∠K = 40°, then find the value of exterior angle formed by extending the side KL

Find the value of ‘x’ in the given figure

If ∆MNO ≅ ∆DEF, ∠M = 60° and ∠E = 45° then find the value of ∠O

In the given figure ray AZ bisects ∠BAD and ∠DCB, prove that ∆BAC ≅ ∆DAC

In the given figure ray AZ bisects ∠BAD and ∠DCB, prove that AB = AD

In the given figure FG = FI and H is midpoint of GI, prove that ∆FGH ≅ ∆FHI

Using the given figure, prove that the triangles are congruent. Can you conclude that AC is parallel to DE

#### Challenge Problems

In the given figure BD = BC, find the value of x

In the given figure find the value of x

In the given figure find the values of x and y

In ∆DEF, ∠F = 48°, ∠E = 68° and bisector of ∠D meets FE at G. Find ∠FGD

In the figure find the value of x

From the given figure find the value of y

## Chapter 4: Geometry

## Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 2 Answers Guide chapter 4 - Geometry

Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 2 Answers Guide chapter 4 (Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 7th Mathematics Term 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Tamil Nadu Board Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 7th Mathematics Term 2 Answers Guide chapter 4 Geometry are Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle, Classification of Triangles (On the Basis of Sides, and of Angles), Equilateral Triangle, Isosceles Triangles, Scalene Triangle, Acute Angled Triangle, Exterior Angle of a Triangle and Its Property, Obtuse Angled Triangle, Right Angled Triangle, Angle Sum Property of a Triangle, Congruence of Triangles, Criteria for Congruence of Triangles, Congruency of Shapes, Congruence Among Line Segments, Congruence of Plane Figures, Congruence of Angles, Congruence of Triangles, SSS Congruence Criterion, SAS Congruence Criterion, ASA Congruence Criterion, RHS Congruence Criterion.

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