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ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) Two line segments are congruent if ……….
(ii) Among two congruent angles, one has a measure of 63°; the measure of the other angle is ……….
(iii) When we write ∠A = ∠B, we actually mean ………
(iv) The side included between ∠M and ∠N of ∆MNP is ……….
(v) The side QR of ∆PQR is included between angles ……….
(vi) If two triangles ABC and PQR are congruent under the correspondence A ↔ R, B ↔ P and C ↔ Q, then in symbolic form it can be written as ∆ABC = ………
(vii) If ∆DEF = ∆SRT, then the correspondence between vertices is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) All circles are congruent.
(ii) Circles having equal radii are congruent.
(iii) Two congruent triangles have equal areas and equal perimeters.
(iv) Two triangles having equal areas are congruent.
(v) Two squares having equal areas are congruent.
(vi) Two rectangles having equal areas are congruent.
(vii) All acute angles are congruent.
(vii)All right angles are congruent.
(ix) Two figures are congruent if they have the same shape.
(x) A two rupee coin is congruent to a five rupee coin.
(xi) All equilateral triangles are congruent.
(xii) Two equilateral triangles having equal perimeters are congruent.
(xii) If two legs of one right triangle are equal to two legs of another right angle triangle, then the two triangles are congruent by SAS rule.
(xiv) If three angles of two triangles are equal, then triangles are congruent.
(xv) If two sides and one angle of one triangle are equal to two sides and one angle of another triangle, then the triangle are congruent.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
Which one of the following is not a standard criterion of congruency of two triangles?
(a) SSS
(b) SSA
(c) SAS
(d) ASA
Solution:

Question 4.
If ∆ABC = ∆PQR and ∠CAB = 65°, then ∠RPQ is
(a) 65°
(b) 75°
(c) 90°
(d) 115°
Solution:

Question 5.
If ∆ABC = ∆EFD, then the correct statement is
(a) ∠A = ∠D
(b) ∠A = ∠F
(c) ∠A = ∠E
(d) ∠B = ∠E
Solution:

Question 6.
If ∆ABC = ∆PQR, then the correct statement is
(a) AB = QR
(b) AB = PR
(c) BC = PR
(d) AC = PR
Solution:

Question 7.
If ∠D = ∠P, ∠E = ∠Q and DE = PQ, then ∆DEF = ∆PQR, by the congruence rule
(a) SAS
(b) ASA
(c) SSS
(d) RHS
Solution:

Question 8.
In ∆ABC and ∆PQR, BC = QR and ∠C = ∠R. To establish ∆ABC = ∆PQR by SAS congruence rule, the additional information required is
(a) AC = PR
(b) AB = PR
(c) CA = PQ
(d) AB = PQ
Solution:

Question 9.
In the given figure, the lengths of the sides of two triangles are given. The correct statement is
(a) ∆ABC = ∆PQR
(b) ∆ABC = ∆QRP
(c) ∆ABC = ∆QPR
(d) ∆ABC = ∆RPQ

Solution:

Question 10.
In the given figure, M is the mid-point of both AC and BD. Then
(a) ∠1 = ∠2
(b) ∠1 = ∠4
(c) ∠2 = ∠4
(d) ∠1 = ∠3

Solution:

Question 11.
In the given figure, ∆PQR = ∆STU. What is the length of TU?
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) cannot be determined

Solution:

Question 12.
In the given figure, ∆ABC and ∆DBC are on the same base BC. If AB = DC and AC = DB, then which of the following statement is correct?
(a) ∆ABC = ∆DBC
(b) ∆ABC = ∆CBD
(c) ∆ABC = ∆DCB
(d) ∆ABC = ∆BCD

Solution:

Question 13.
The two triangles shown in the given figure are:
(a) congruent by AAS rule
(b) congruent by ASA rule
(c) congruent by SAS rule
(d) not congruent.

Solution:

Question 14.
In .the given figure, ∆ABC = ∆PQR. The values of x and y are:
(a) x = 63, y = 35
(b) x = 77, y = 35
(c) x = 35, y = 77
(d) x = 63, y = 40

Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
If all the three altitudes of a triangle are equal, then prove that it is an equilateral triangle.
Solution:

Question 2.
In the given fig., if BA || RP, QP || BC and AQ = CR, then prove that ∆ABC = ∆RPQ.

Solution:

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles Ex 12.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.2

Question 1.
You want to establish ΔDEF = ΔMNP, using ASA rule of congruence. You are given that ∠D = ∠M and ∠F = ∠P. What additional information is needed to establish the congruence?
Solution:

Question 2.
In the given figure, two triangles are congruent. The corresponding parts are marked. We can write ΔRAT =?

Solution:

Question 3.
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Solution:

Question 4.
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by ASA congruence rule. In the case of congruence, write its in symbolic form.

Solution:

Question 5.
In the adjoining figure, measures of some parts are indicated.
(i) State three pairs of equal parts in triangles ABC and ABD.
(ii) Is ΔABC = ΔBAD? Give reasons.
(iii) Is BC = AD? Why?

Solution:

Question 6.
In the adjoining figure, ray AZ bisects ∠DAB as well as ∠DCB.
(i) State the three pairs of equal parts in triangles BAC and DAC.
(ii) Is ΔBAC = ΔDAC? Give reasons.
(iii) Is CD = CB? Give reasons.

Solution:

Question 7.
Explain why ΔABC = ΔFED?

Solution:

Question 8.
Given below are the measurements of some parts of triangles. Examine whether the two triangles are congruent or not, using RHS congruence rule. In the case of congruent triangles, write the result in symbolic form

Solution:

Question 9.
In the given figure, measurements of some parts are given.
(i) State the three pairs of equal parts in ΔPQS and ΔPRS.
(ii) Is ΔPQS = ΔPRS? Give reasons.
(iii) Is S mid-point of \(\bar { QR }\) ? Why?

Solution:

Question 10.
In the given figure, O is mid-point of \(\bar { AB }\) and ∠A = ∠B. Show that ΔAOC = ΔBOD.

Solution:

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles Ex 12.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1

Question 1.
If ΔABC and ΔDEF are congruent under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Solution:

Question 2.
If ΔDEF = ΔBCA, then write the part(s) of ΔBCA that correspond to
(i) ∠E
(ii) \(\bar { EF }\)
(iii) ∠F
(iv) \(\bar { DF }\)
Solution:

Question 3.
In the figure given below, the lengths of the sides of the triangles are indicated. By using SSS congruency rule, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form:

Solution:

Question 4.
In the given figure, AB = 5 cm, AC = 5 cm, BD = 2.5 cm and CD = 2.5 cm
(i) State the three pairs of equal parts in ΔADB and ΔADC
(ii) Is ΔADB = ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Why?

Solution:

Question 5.
In the given figure, AB = AC and D is the mid-point of \(\bar { BC }\).
(i) State the three pairs of equal parts in ΔADB and ΔADC.
(ii) Is ΔADB = ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Why?

Solution:

Question 6.
In the figure given below, the measures of some parts of the triangles are indicated. By using SAS rule of congruency, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form.

Solution:

Question 7.
By applying SAS congruence rule, you want to establish that ΔPQR = ΔFED. If is given that PQ = EF and RP = DF. What additional information is needed to establish the congruence?
Solution:

Question 8.
You want to show that ΔART = ΔPEN

(a) If you have to use SSS criterion, then you need to show
(i) AR = ……….
(ii) RT = ……….
(iii) AT = …………
(b) If it is given that ∠T = ∠N and you are to use the SAS criterion, you need to have
(i) RT = ………. and (ii) PN = ……….
Solution:

Question 9.
You have to show that ΔAMP = ΔAMQ.
In the following proof, supply the missing reasons.

Solution:

Question 10.Solution:
In the given figure:
(i) State three pairs of equal parts in ΔPSR and ΔRQP.
(ii) Is ΔPSR = ΔRQP? Give reasons
(iii) Is PS = RQ? Why?
(iv) Is ∠S = ∠Q? Why?

Solution:

Question 11.
In the given figure, AB = DC and ∠ABC = ∠DCB.
(i) State three pairs of equal parts in AABC and ADCB.
(ii) Is ΔABC = ΔDCB? Give reasons.
(iii) Is AC = DB? Why?

Solution:

Question 12.
In the quadrilateral, AC = AD, and AB bisect ∠CAD.
(i) State three pairs of equal parts in ΔABC and ΔABD.
(ii) Is ΔABC = ΔABD? Give reasons.
(iii) Is BC = BD? Why?
(iv) Is ∠C = ∠D? Why?

Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Check Your Progress

Question 1.
Find the value of x in each of the following diagrams:

Solution:

Question 2.
In the given figure, ∠B = 70° and ∠A = 50°. If the bisector of ∠C meets AB in D, then find ∠ADC.

Solution:

Question 3.
Find the values of x and y in each of the following figures:

Solution:

Question 4.
If the two acute angles of a right-angled triangle are in the ratio 7 : 8, find these angles.
Solution:

Question 5.
If the angles of a triangle are (3x)°, (2x – 7)° and (4x – 11)°, then find the value of x.
Solution:

Question 6.
In an isosceles triangle, the vertical angle is 15° greater than each of its base angles. Find all the angles of the triangle.
Solution:

Question 7.
Can a triangle have three sides whose lengths are
(i) 4.5 cm, 3.8 cm, 7.2 cm?
(ii) 3.2 cm, 5.3 cm, 9.4 cm?
Solution:

Question 8.
If the lengths of two sides of a triangle are 5 cm and 12 cm, then what can be the length of the third side?
Solution:

Question 9.
In the given figure, all measurements are in centimeters. If AD is perpendicular to BC, find the length of AB.

Solution:

Question 10.
In the given figure, AB and CD are two vertical poles of height 19 m and 11 m respectively. If the shortest distance between their tops is 17 m, find how far apart they are?

Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A triangle has at least ………… acute angles.
(ii) A triangle cannot have more than ……… right angle.
(iii) A triangle cannot have more than ………… obtuse angle.
(iv) In every triangle, the sum of (interior) angles of a triangle = ……….. right angles.
(v) In every triangle, an exterior angle + adjacent interior angle = ………… degrees.
(vi) In every triangle, an exterior angle = sum of the …….. interior opposite angles.
(vii) In a right-angled triangle, if one of the acute angles measures 25° then the measure of the other acute angle is …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) A triangle can have all three angles with a measure greater than 60°.
(ii) A triangle can have all three angles with a measure of less than 60°.
(iii) If an exterior angle of a triangle is a right angle, then each of its interior opposite angles is acute.
(iv) In a right-angled triangle, the sum of two acute angles is 90°.
(v) If all the three sides of a triangle are equal, then it is called a scalene triangle.
(vi) Every equilateral triangle is an isosceles triangle.
(vii) Every isosceles triangle must be an equilateral triangle.
(viii) Each acute angle of an isosceles right-angled triangle measures 60°.
(ix) A median of a triangle always lies inside the triangle.
(x) An altitude of a triangle always lies outside the triangle.
(xii) In a triangle, the sum of squares of two sides is equal to the square of the third side.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 17):
Question 3.
A triangle formed by the sides of lengths 4.5 cm, 6 cm, and 4.5 cm is
(a) scalene
(b) isosceles
(c) equilateral
(d) none of these
Solution:

Question 4.
The number of medians in a triangle is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 5.
An exterior angle of a triangle is 125°. If one of the two interior opposite angles is 55° then the other interior opposite angle is
(a) 70°
(b) 55°
(c) 60°
(d) 80°
Solution:

Question 6.
In a ∆ABC, if ∠A = 40° and ∠B = 55° then ∠C is
(a) 75°
(b) 80°
(c) 95°
(d) 85°
Solution:

Question 7.
If the angles of a triangle are 35°, 35°, and 110°, then it is
(a) an isosceles triangle
(b) an equilateral triangle
(c) a scalene triangle
(d) right-angled triangle
Solution:

Question 8.
A triangle whose two angles measure 30° and 120° is
(a) scale
(b) isosceles
(c) equilateral
(d) none of these
Solution:

Question 9.
A triangle can have two
(a) right angles
(b) obtuse angles
(c) acute angles
(d) straight angles
Solution:

Question 10.
A triangle whose angles measure 35°, 35° and 90° is
(a) acute-angled
(b) right-angled
(c) obtuse-angled
(d) isosceles
Solution:

Question 11.
A triangle is not possible whose angles measure
(a) 40°, 65°, 75°
(b) 50°, 56°, 74°
(c) 72°, 63°, 45°
(d) 67°, 42°, 81°
Solution:

Question 12.
If in an isosceles triangle, each of the base angles is 40°, then the triangle is
(a) right-angled triangle
(b) acute-angled triangle
(c) obtuse-angled triangle
(d) isosceles right-angled triangle
Solution:

Question 13.
A triangle is not possible with sides of lengths (in cm)
(a) 6, 4, 10
(b) 5, 3, 7
(c) 7, 8, 9
(d) 3.6, 5.4, 8
Solution:

Question 14.
Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm?
(a) 32 cm
(b) 3 cm
(c) 4 cm
(d) 5 cm
Solution:

Question 15.
In a right-angled triangle, the lengths of two leg’s are 6 cm and 8 cm. The length of the hypotenuse is
(a) 14 cm
(b) 10 cm
(c) 11 cm
(d) 12 cm
Solution:

Question 16.
If the dimensions of a rectangle are 15 m and 8 m, then the length of a diagonal is
(a) 7 m
(b) 23 m
(c) 17 m
(d) 20 m
Solution:

Question 17.
If p, q, and r are the lengths of the three sides of a triangle, then which of the following statements is correct?
(a) p + q = r
(b) p + q < r (c) p + q > r
(d) p – q > r
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
In ∆DEF, DM and EN are two medians. Prove that 3(DF + EF) > 2(DM + EN).
Solution:

Question 2.
In a ∆ABC, medians AD, BE and CF intersect each other at point G. Prove that 3(AB + BC + CA) > 2(AD + BE + CF).
Solution: