Triangles Class 9 Worksheet 1 with Answers
1. In the given figure, find the angle marked as
x.
2.
Find whether the triangle is right-angled, for
the sides of the given length.
a. 15, 17, 10 b. 6, 8, 10 c. 13, 8, 15
3. Two poles 16 m and 10 m high stands upright on
a ground. If the distance between their feet is 8 m, then find the distance
between their tops.
4. In the given figure, ABC is a triangle in which AB = AC. If BC is produced to D, prove that AD > AC.
5. The length of the sides of some triangles is given below. Which of
them is right-angled? In case of right-angled, name the angle that measures 90°.
a.
XY = 12 cm, YZ = 20 cm, ZX = 16 cm
b. DE = 4.1 cm,
FD = 0.9 cm, EF = 4.0 cm
6.
State true or false.
a.
The angles of a triangle are 90°, 30°, 90°.
b.
A triangle can have two obtuse angles.
c.
In ΔABC, BC > AC implies ∠A > ∠B.
d.
The point of concurrency of three medians of a triangle is a centroid.
e. A scalene
triangle can be equiangular.
7. What is the correct order of angles of ΔABC from the smallest to the greatest?
8. In the given figure, AB⊥BC and ED⊥FD such that BA = DE and BF = DC.
Prove that ΔABC ≅ ΔDEF
and hence show that AC = EF.
9. The given figure shows the part of roof structure of a school. Show that PQ = PS.
10. In
the given figure, ABC is an isosceles triangle with AB = AC and also given that
BD = EC. Prove that AE = AD.
11.
A tree breaks at a point but did not separate.
Its top touches the ground at a distance of 12 m from its base. If it broke at
a height of 5 m from the ground, what was the actual height of the tree before
it broke?
Triangles Class 9 Worksheet 2 with Answers
1.
One of the exterior angles of a triangle is 80°
and the interior opposite angles are in the ratio 3 : 5. Find the angles of the
triangle.
2. ABC
is an isosceles triangle, right-angled at C. Prove that AB2 = 2AC2.
3.
ABC is a triangle in which AB = AC. P is any
point in the interior of the triangle such that ∠ABP = ∠ACP. Prove that AP bisects ∠BAC.
4.
In the given figure, ΔABC is right-angled at C
and CD ⊥ AB. Also ∠A = 65°. Find:
a.
∠ACD
b.
∠CBD
c. ∠BCD
5.
In the given figure, prove that
∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 360°.
6. Compute
the value of x in each of the following:
7.
Two poles of height 9 m and 14 m stand on a
plane ground. If the distance between their feet is 12 m, find the distance
between their tops.
8.
Fill in the blanks.
a.
An exterior angle of a triangle is equal to the sum of the _________.
b.
In a triangle, if two sides are equal, then the _________ opposite to those
sides are equal.
c.
In a triangle, sum of any two sides of a triangle is always _________ the third
side.
d.
Two rectangles are congruent if they have the same _________.
e. Two circles are congruent if they have the
same _________.
9. In
the given figure, find ∠ABD. Also, if ∠C
= 3 ∠ABC, find ∠ABC.
10.
The ratio between the vertical angle and the
base angle of an isosceles triangle is 2 : 5. Find the angles of the triangle.
11. AD, BE and CF are the altitudes of ΔABC which are equal. Prove that ΔABC is an equilateral triangle.
ANSWERS
Worksheet 1
1. 130°
2. a. No b. Yes
c. No
3. 10 m
5. a. Right-angled; ∠X
b. Right-angled; ∠F
6. a. False b. False
c. True d. True
e. False
7. ∠B < ∠A < ∠C
8. Do it yourself
9. Do it yourself
10. Do it yourself
11. 18 m
Worksheet 2
1. 30°, 50°, 100°
2. Do it yourself
3. Do it yourself
4. a. 25° b. 25°
c. 65°
5. Do it yourself
6. a. 88° b. 125°
7. 13 m
8. a. opposite interior angles
b. angles c. greater than
d. dimensions e. radii
9. 30°; 20°
10. 75°; 75°; 30°
11. Do it yourself
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| Maths Worksheets for Other Chapters of Class 9 |
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3. Area of parallelograms and triangles worksheets
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6. Polynomials class 9 worksheets
7. Coordinate geometry class 9 worksheets
8. Linear equations in two variables class 9 worksheets
9. Introduction to Euclid’s geometry class 9 worksheets
10. Lines and angles class 9 worksheets
11. Quadrilaterals class 9 worksheet
12. Heron’s formula class 9 worksheet
13. Statistics class 9 worksheets
14. Probability class 9 worksheet
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