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Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Unit Test: Triangles
Unit Test: Triangles | Mathematics (Maths) Class 10 PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
- Question numbers 1 to 5 carry 1 mark each.
- Question numbers 6 to 8 carry 2 marks each.
- Question numbers 9 to 11 carry 3 marks each.
- Question numbers 12 & 13 carry 5 marks each.
Q1. In ΔPQR, if PS is the internal bisector of ∠P meeting QR at S and PQ = 15 cm, QS = (3 + x) cm, SR = (x – 3) cm and PR = 7 cm, then find the value of x. (1 Mark)
(a) 2.85 cm
(b) 8.25 cm
(c) 5.28 cm
(d) 8.52 cm
Q2: If ABC and DEF are two triangles and AB/DE=BC/FD, then the two triangles are similar if (1 Mark)
(a) ∠A=∠F
(b) ∠B=∠D
(c) ∠A=∠D
(d) ∠B=∠E
Q3: If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then (1 Mark)
(a) ΔPQR ~ ΔCAB
(b) ΔPQR ~ ΔABC
(c) ΔCBA ~ ΔPQR
(d) ΔBCA ~ ΔPQR
Q4: Write the truth value (T/F) of each of the following statements : (1 Mark)
(i) Any two similar figures are congruent.
(ii)Two polygons are similar, if their corresponding sides are proportional.
Q5: D and E are respectively the points on sides AB and AC of triangle ABC such that AB = 3 cm, BD = 1.5 cm, BC = 7.5 cm, and DE || BC. What is the length of DE? (1 Mark)
(a) 2 cm
(b) 2.5 cm
(c) 3.75 cm
(d) 3 cm
Q6: In the figure, DE // AC and DF // AE. Prove that BF/FE = BE/EC. (2 Marks)
Q7: In the figure, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm. (2 Marks)
Q8: In the given figure, XY || QR,
and PR = 6.3 cm, find YR. (2 Marks)
Q9: D and E are points on sides AB and AC of triangle ABC such that DE || BC. If AD = 2·4 cm, DB = 3.6 cm and AC = 5 cm, find AE. (3 Marks)
Q10: X and Y are points on the sides AB and AC respectively of a triangle ABC such that 
, AY = 2 cm and YC = 6 cm. Find whether XY || BC or not. (3 Marks)
Q11: If a line segment intersects sides AB and AC of a ∆ABC at D and E respectively and is parallel to BC, prove that
. (3 Marks)
Q12: In the given figure, altitudes AD and CE of ∆ ABC intersect each other at the point P. Show that: (5 Marks)
(i) ∆AEP ~ ∆ CDP
(ii) ∆ABD ~ ∆ CBE
(iii) ∆AEP ~ ∆ADB
(iv) ∆ PDC ~ ∆ BEC
Q13: In given figure, EB ⊥ AC, BG ⊥ AE and CF ⊥ AE. (5 Marks)
Prove that:
(a) ∆ABG ~ ∆DCB
(b) 
You can find the solutions of this Unit Test here: Unit Test (Solutions): Triangles
The document Unit Test: Triangles | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Unit Test: Triangles - Mathematics (Maths) Class 10
| 1. What are the different types of triangles based on their sides? |  |
| 2. How do you determine if three lengths can form a triangle? | |
Ans. To determine if three lengths can form a triangle, you can use the triangle inequality theorem. The sum of the lengths of any two sides must be greater than the length of the third side for all three combinations.
| 3. What are the types of triangles based on their angles? | |
Ans. Triangles can also be classified based on their angles into three types: acute triangles (all angles less than 90 degrees), right triangles (one angle exactly 90 degrees), and obtuse triangles (one angle greater than 90 degrees).
| 4. How do you calculate the area of a triangle? | |
Ans. The area of a triangle can be calculated using the formula: Area = 1/2 × base × height. You can also use Heron's formula if you know all three side lengths.
| 5. What is the Pythagorean theorem and how does it apply to right triangles? | |
Ans. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is expressed as a² + b² = c², where c is the hypotenuse.
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