Chapter 6: Triangles

Q41Written answer

In ∆ABC, ∠Α = 50°, ∠B = 70° and the bisector of ∠C meets AB in D (Fig. 6.17). The measure of ∠ADC is

NCERT Exemplar Class 7 Maths Solutions Chapter 6 Image 17

(a) 50° (b) 100° (c) 30° (d) 70°

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Solution:-

(b) 100^o

From the figure,

Consider the ΔABC,

We know that, sum of angles of triangle is equal to 180^o.

So, ∠Α + ∠B + ∠C = 180^o

50^o + 70^o + ∠C = 180^o

∠C + 120^o = 180^o

∠C = 180^o – 120^o

∠C = 60^o

Since CD bisects ∠C,

So, ∠DCB = ∠ΑCD = ½ ∠C

= 60^o/2

= 30^o

Now, consider ΔBDC

From exterior angle property, ∠ADC = ∠DBC + ∠DCB

∠ADC = 70^o + 30^o

= 100^o

Q42Written answer

If for ∆ABC and ∆DEF, the correspondence CAB ↔ EDF gives a congruence, then which of the following is not true?

(a) AC = DE (b) AB = EF (c) ∠A = ∠D (d) ∠C = ∠E

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Solution: –

(b) AB = EF

Because, for ∆ABC and ∆DEF AB = DF

Q43Written answer

In Fig. 6.18, M is the mid-point of both AC and BD. Then

(a) ∠1 = ∠2 (b) ∠1 = ∠4 (c) ∠2 = ∠4 (d) ∠1 = ∠3

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Solution: –

(b) ∠1 = ∠4

From the figure, M is the mid-point of both AC and BD.

By the corresponding parts of congruent triangles, ∠1 = ∠4.

Q44Written answer

If D is the mid-point of the side BC in ∆ABC where AB = AC, then ∠ADC is

(a) 60° (b) 45° (c) 120s° (d) 90°

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Solution:-

(d) 90^o

We know that, in an isosceles triangle, altitude and median are the same.

From the question, if D is the mid-point of the side BC in ∆ABC

Where, D is midpoint of BC joining from point A gives AD as median.

It possess 90^o angle on BC

Therefore, ∠ADC = 90^o

Q45Written answer

Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the

(a) RHS congruence criterion

(b) ASA congruence criterion

(c) SAS congruence criterion

(d) AAA congruence criterion

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Solution:-

(b) ASA congruence criterion

Q46Written answer

By which congruency criterion, the two triangles in Fig. 6.19 are congruent?

(a) RHS (b) ASA (c) SSS (d) SAS

NCERT Exemplar Class 7 Maths Solutions Chapter 6 Image 19

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Solution:-

(c) SSS

Under a given correspondence, two triangles are congruent, if the three sides of the one are equal to the three sides of the other.

Q47Written answer

By which of the following criterion two triangles cannot be proved congruent?

(a) AAA (b) SSS (c) SAS (d) ASA

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Solution: –

(a) AAA

In AAA criterion, two triangles cannot be proved congruent.

Q48Written answer

If ∆PQR is congruent to ∆STU (Fig. 6.20), then what is the length of TU?

(a) 5 cm (b) 6 cm (c) 7 cm (d) cannot be determined

NCERT Exemplar Class 7 Maths Solutions Chapter 6 Image 20

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Solution:-

(b) 6 cm

From the question it is given that,

Δ PQR ≅ Δ STU

So,

PQR ↔ STU

∴ QR = TU

TU = 6cm

Q49Written answer

If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then which of the following gives a congruence relationship?

(a) ∆ ABC ≅ ∆ DBC (b) ∆ ABC ≅ ∆CBD

(c) ∆ ABC ≅ ∆ DCB (d) ∆ ABC ≅ ∆BCD

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Solution:-

(c) ∆ ABC ≅ ∆ DCB

Consider the ΔABC and ΔDCB,

From the question it is given that, AB = DC and AC = DB

BC = BC … [because common side]

Therefore, ∆ ABC ≅ ∆ DCB

In questions 50 to 69, fill in the blanks to make the statements true.

Q50Written answer

The triangle always has altitude outside itself.

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Solution:-

The Obtuse triangle always has altitude outside itself.

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