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## Andhra Pradesh State Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.1 Books Solutions

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## AP State Syllabus 9th Class Maths Solutions 8th Lesson Quadrilaterals Exercise 8.1

Question 1.
State whether the statements are true or false.
i) Every parallelogram is a trapezium.
iii) All trapeziums are parallelograms.
iv) A square is a rhombus.
v) Every rhombus is a square.
vi) All parallelograms are rectangles.
Solution:
i) True
ii) True
iii) False
iv) True
v) False
vi) False

Question 2.
Complete the following table by writing YES if the property holds for the particular quadrilateral and NO if property does not holds.

Solution:

Question 3.
ABCD is a trapezium in which AB || CD. If AD = BC, show that ∠A = ∠B and ∠C = ∠D.
Solution:
Given that in □ABCD AB || CD; AD = BC
Mark a point ‘E’ on AB such DC = AE.

Join E, C.
AE // DC and AE = DC
∴ □AECD is a parallelogram.
∠DAE = ∠CEB (corresponding angles) ……………..(1)
In ΔCEB; CE = CB (∵ CE = AD)
∴ ∠CEB = ∠CBE (angles opp. to equal sides) …………….. (2)
From (1) & (2)
∠DAE = ∠CBE
⇒ ∠A = ∠B
Also ∠D = ∠AEC (∵ Opp. angles of a parallelogram)
= ∠ECB + ∠CBE [ ∵ ∠AEC is ext. angle of ΔBCE] |
= ∠ECB + ∠CEB [ ∵∠CBE = ∠CEB]
= ∠ECB + ∠ECD [∵ ∠ECD = ∠CEB alt. int. angles]
= ∠BCD = ∠C
∴ ∠C = ∠D

Question 4.
The four angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. Find the measure of each angle of the quadri-lateral.
Solution:
Given that, the ratio of angles of a quad-rilateral = 1 : 2 : 3 : 4
Sum of the terms of the ratio
= 1 +2 + 3 + 4= 10
Sum of the four interior angles of a quadrilateral = 360°
∴ The measure of first angle
= 110 × 360° = 36°
The measure of second angle
= 210 × 360° = 72°
The measure of third angle
= 310 × 360° = 108°
The measure of fourth angle
= 410 × 360° = 144°

Question 5.
ABCD is a rectangle, AC is diagonal. Find the angles of ΔACD. Give reasons.
Solution:

Given that □ABCD is a rectangle;
AC is its diagonal.
In ΔACD; ∠D = 90° [ ∵ ∠D is also angle of the rectangle]
∠A + ∠C = 90° [ ∵ ∠D = 90° ⇒ ∠A + ∠C = 180°-90° = 90°]
(i.e,,) ∠D right angle and
∠A, ∠C are complementary angles.

## Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.1 Textbooks for Exam Preparations

Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.1 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 8 Quadrilaterals Ex 8.1 exam preparation. The AP Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.1 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 8 Quadrilaterals Ex 8.1 Books State Board syllabus with maximum efficiency.

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