CBSE Class 9 Mathematics Triangles Assignment Set A

CBSE Class 9 Mathematics Triangles Assignment Set A. Students are advised to refer to the attached assignments and practise them regularly. This will help them to identify their weak areas and will help them to score better in examination. Parents should download and give the assignments to their children for practice.

ASSERTION & REASONING QUESTIONS
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R) . Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion : If angles ‘a ’ and ‘b’ form a linear pair of angles and a = 400, then b = 1500.
Reason : Sum of linear pair of angles is always 1800
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the sum of linear pair of angles is always 1800.
So, Reason is correct.
Now, a + b = 400 + 1500 = 1900 ≠1800
Hence, Assertion is not correct
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion : Supplement of angle is one fourth of itself. The measure of the angle is 1440.
Reason : Two angles are said to be supplementary if their sum of measure of angles is 1800.
Answer : We know that two angles are said to be supplementary if their sum of
measure of angles is 1800.
So, Reason is correct.
Let the angle be x . Supplement of x(1/4) x
so, x + 1/4 x = 180i^o ⇒ 5/4 x = 180^o ⇒ x = 144^o
So, Assertion is also correct
Also, reason (R) is the correct explanation of assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion: The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle of the triangle is 800.
Reason: The sum of all the interior angles of a triangle is 1800
Answer : We know that the sum of all the interior angles of a triangle is 1800.
So, Reason (R) is true.
Let the angles of a triangle be 2x, 3x and 4x then we have
2x + 3x + 4x = 1800
⇒ 9x = 1800
⇒ x = 200.
Hence, Largest angle = 4 x 200 = 800.
So, Assertion (A) is also true.
Also, Reason (R) is a correct explanation of Assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. Assertion : Sum of the pair of angles 1200 and 600 is supplementary.
Reason : Two angles, the sum of whose measures is 1800, are called supplementary angles.
Answer : We know that two angles are said to be supplementary if their sum of measure of angles is 1800.
So, Reason is correct.
Now, 1200 + 600 = 1800 ⇒ Sum of the pair of angles 1200 and 600 is supplementary.
So, Assertion is also correct
Also, reason (R) is the correct explanation of assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : The angles of a triangle are in the ration 3 : 5 : 7. The triangle is acuteangled
Reason : The sum of angles that are formed on a straight line is equal to 180°.
Answer : We know that the sum of angles that are formed on a straight line is equal to 180°.
So, Reason is correct
Also, the sum of all the interior angles of a triangle is 1800
Let the angles measure (3x) °, (5x) ° and (7x) °.
Then,3x + 5x + 7x = 180°   ⇒ 15x = 180° ⇒x = 12°
Therefore, the angles are 3(12) °=36°, 5(12) °=60° and 7(12) ° = 84°.
Hence, the triangle is acute-angled.
So, Assertion (A) is also true.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : If two internal opposite angles of a triangle are equal and external angle is given to be 1100, then each of the equal internal angle is 550.
Reason : A triangle with one of its angle 900, is called a right triangle.
Answer : For Assertion: We know that the exterior angle is equal to the sum of its interior opposite angles. So, x + x = 1100.
⇒ 2x = 1100
⇒ x = 550
So, Assertion is correct
Also, we know that a triangle with one of its angle 900, is called a right triangle.
So, Reason is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : An angle is 140 more than its complementary angle, then angle is 520.
Reason : Two angles are said to be supplementary if their sum of measure of angles is 1800.
Answer : We know that two angles are said to be supplementary if their sum of measure of angles is 1800.
So, Reason is correct.
Let the angle be x . Complement of x = (900 - x)
Since, the difference is 140, we have x – (900 – x) = 140
⇒ 2x = 1040
⇒ x = 520
So, Assertion is also correct
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion: In the given figure, AOB is a straight line. If ∠AOC = (3x + 10) ° and ∠BOC (4x − 26) °, then ∠BOC = 860
Reason: The sum of angles that are formed on a straight line is equal to 180°.
Answer : We know that the sum of angles that are formed on a straight line is equal to 180°.
So, Reason is correct
We have : ∠AOC+∠BOC=180° [Since AOB is a straight line ]
⇒3x + 10 + 4x − 26 = 180°
⇒7x = 196°
⇒x = 28°
∴∠BOC = [4 × 28 − 26]°
⇒∠BOC=86°.
So, Assertion (A) is also true.
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the greater of the two angles is 1000.
Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 1800.
Answer : We know If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 1800 hat the solution of the line will satisfy the equation of the line.
So, Reason is correct.
Let the angles be 5x and 4x
Since, these two angles are co-interior angles. So, we
have 5x + 4x = 1800   ⇒ 9x = 1800 ⇒ x = 200
Hence, greater angle = 5x = 5 x 200 = 1000
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : A triangle can have two obtuse angles.
Reason : The sum of all the interior angles of a triangle is 1800
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the sum of all the interior angles of a triangle is 1800.
So, Reason (R) is true.
Since the Sum of two obtuse angles will be more than 1800.
So, Assertion (A) is false.
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion: The value of x from the adjoining figure, if l || m is 150.
Reason: If two parallel lines are intersected by a transversal, then each pair of corresponding angles so formed is equal.
Answer : We know that If two parallel lines are intersected by a transversal,
then each pair of corresponding angles so formed is equal.
So, Reason is correct.
Also, we know that If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 1800.
From figure we have, 1200 – x + 5x = 1800
⇒ 4x = 1800 – 1200
⇒ 4x = 600
⇒ x = 150
So, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and
reason (R) is not the correct explanation of assertion (A) .

SECTION A: (1 MARK)

1. In ΔPQR if ∠QPR = 80° and PQ = PR, find ∠R and ∠Q (CCE 2010)

2. In the given fig 1, Mention the congruency rule used in proving ΔACB  ΔACD

3. In the given figures, BD and YE are the medians.

Find the value of YZ.(State the reasons)

Fig1

SECTION B: (2 MARKS)

4. Line segments AB and CD intersect at M. If ACǁDB and M is midpoint of AB. Prove

that M is midpoint of CD. (CCE 2010)

5. In the given figure, RV = VT, QV = VU, VR⊥SQ and VT⊥SU. Prove that SQ =SU.

Fig 5.

6. In ΔPSR, Q is a point on SR such that PQ = PR, show that PS > PQ.

7. In fig5, AB =PQ, ∠A =∠P and ∠ACD = ∠PRS. Prove that ΔABC  ΔPQR.

8. In ΔABC, AD is the bisector of ∠BAC. Prove that AB > BD.

SECTION C: (3 MARKS)

9. ABCD is a square. X and Y are points on the sides AD and BC such that AY = BX. Prove that ∠XAY = ∠ YBX. (CCE 2013)

10. In fig 2., AD = BC and BD = AC , prove that ∠DAB = ∠CBA (CCE 2014)

11. In fig3., l ǁ m and p ǁ q . Show that ΔABC  ΔCDA.

Fig 4.

12. In the given fig, ΔABC and ΔDBC are two isosceles triangle on the same base BC . If ∠BDC =120° and ∠ABD = 40°, then find ∠BAC and ∠ADC. (CCE 2010)

SECTION D: (4 MARKS)

13. ABC is a triangle and D is the midpoint of BC. The perpendiculars from D to AB and AC are equal. Prove that triangle is isosceles. (CCE 2013)

14. Two sides AB and BC and median AM of ΔABC are respectively equal to sides PQ, QR and median PN of ΔPQR then prove that ΔABC  ΔPQR.

15. In the given figure, AD and CE are the bisectors of ∠A and ∠C respectively. If ∠ABC = 90°, find ∠ADC + ∠AEC. (CCE 2015)

16. Show that in a quadrilateral ABCD , AB + BC + CD +DA < 2 (BD + AC)

Please click the link below to download CBSE Class 9 Mathematics Triangles Assignment Set A.