NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 6: Triangles

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The Obtuse triangle always has altitude outside itself.

The sum of an exterior angle of a triangle and its adjacent angle is always a right angle.

The longest side of a right angled triangle is called its hypotenuse.

Median is also called altitude in an equilateral triangle.

Measures of each of the angles of an equilateral triangle is 60°.

In an isosceles triangle, two angles are always equal.

In an isosceles triangle, angles opposite to equal sides are equal.

If one angle of a triangle is equal to the sum of other two, then the measure of that angle is 90°.

Every triangle has at least two acute angle(s).

Two line segments are congruent, if they are of equal lengths.

Two angles are said to be congruent, if they have equal measures.

Two rectangles are congruent, if they have same length and breadth.

Two squares are congruent, if they have same side.

(i) ∠R = ∠Z

(ii) QR = XZ

(iii) ∠P = ∠Y

(iv) QP = XY

(v) ∠Q = ∠X

(vi) RP = ZY

In Fig. 6.22, ΔPQR ≅ Δ XZY

In Fig. 6.23, ΔPQR ≅ Δ RSP

In Fig. 6.24, Δ DRQ ≅ Δ PQR

In Fig. 6.25, ΔARO ≅ Δ PQO

(i) Δ ADC ≅ ΔABC

(ii) BC = DC

(iii) ∠BCA = ∠DCA

(iv) Line segment AC bisects ∠BAD and ∠BCD

(i) ∠TPQ = ∠PQR + ∠PRQ

(ii) ∠UQR = ∠QRP + ∠PQR

(iii) ∠PRS = ∠QRP + ∠QPR