R S Aggarwal Solutions for Class 10 Maths helps students develop a strong foundational base for all the important concepts. R S Aggarwal Solutions for class 10 Maths chapter 7 exercise 7E is available here. These solutions are available in PDF format and students can freely download it by clicking on the click below.
Access other exercise solutions of Class 10 Maths Chapter 7 Triangles
Question 1: State the two properties which are necessary for given two triangles to be similar.
Two properties for similarity of two triangles are:
(i) Angle-Angle-Angle (AAA) property.
(ii) Angle-Side-Angle (ASA) property.
Question 2: State the basic proportionality theorem.
In a triangle, if a line parallel to one side is drawn, it will divide the other two sides proportionally.
Question 3: State the converse of Thales’ theorem.
If a line divides any two sides of a triangle in the same ratio. Then, the line must be parallel to the third side.
Question 4: State the midpoint theorem.
The line joining the midpoints of two sides of a triangle, is parallel to the third side.
Question 5: State the AAA-similarity criterion.
In two triangles, if three angles of the one triangle are equal to the three angles of the other, the triangles are similar.
Question 6: State the AA-similarity criterion.
In two triangles, if two angles of the one triangle are equal to the corresponding angles of the other triangle, then the triangles are similar.
Question 7: State the SSS-criterion for similarity of triangles.
In two triangles, if three sides of the one are proportional to the corresponding sides of the other, the triangles are similar.
Question 8: State the SAS-similarity criterion.
In two triangles, if two sides of the one are proportional to the corresponding sides of the other and their included angles are equal, the two triangles are similar.
Question 9: State Pythagoras’ theorem.
In a right angled triangle, the square on the hypotenuse is equal to the sum of squares on the other two sides.
Question 10: State the converse of Pythagoras theorem.
In a triangle, if the square on the longest side is equal to the sum of the squares on the other two sides, then the angle opposite to the hypotenuse is a right angle.
Question 11: If D, E and F are respectively the midpoints of sides AB, BC and CA of ∆ABC then what is the ratio of the areas of ∆DEF and ∆ABC?
The ratio of their areas will be 1 : 4.
Question 12: Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A = 70°, PR = 9 cm, ∠P = 70° and PQ = 4.5 cm. Show that ∆ABC ~ ∆PQR and state the similarity criterion.
In two triangles ∆ABC and ∆PQR,
AB = 3 cm, AC = 6 cm, ∠A = 70°
PR = 9 cm, ∠P = 70° and PQ= 4.5 cm
∠A = ∠P = 70° (Same)
AC/PR = 6/9 = 2/3 and
AB/PQ = 3/4.5 = 2/3
=> AC/PR = AB/PQ
Both ∆ABC and ∆PQR are similar.
Question 13: If ∆ABC ~ ∆DEF such that 2AB = DE and BC = 6 cm, find EF.
∆ABC ~ ∆DEF (given)
2AB = DE, BC = 6 cm (given)
∠E = ∠B and ∠D = ∠A and ∠F = ∠C
2AB = DE
=> AB/DE = 1/2
AB/DE = BC/EF
1/2 = 6/EF
or EF = 12 cm
Question 14: In the given figure, DE || BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.
DE || BC
AD = x cm, DB = (3x + 4) cm
AE = (x + 3) cm and EC = (3x + 19) cm
AD/DB = AE/EC
x/(3x+4) = (x+3)/(3x+19)
3x2 + 19x – 3x2– 9x – 4x = 12
x = 2
Question 15: A ladder 10 m long reaches the window of a house 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.
Let AB is the ladder and A is window.
Then, AB = 10 m and AC = 8 m
Let BC = x
In right ∆ABC,
By Pythagoras Theorem:
AB2 = AC2 + BC2
(10)² = 8² + x²
100 = 64 + x²
x² = 100 – 64 = 36
or x = 6
Therefore, Distance between foot of ladder and base of the wall is 6 m.
R S Aggarwal Solutions for Class 10 Maths Chapter 7 Triangles Exercise 7E
Class 10 Maths Chapter 7 Triangles Exercise 7E is based on the topics:
- Similar Triangles
- Thales’ Theorem and it’s converse
- Midpoint theorem
- Similarity of two triangles
- Similarity of two triangles and its results.