Page 195 - ICSE Math 7

D C

6. In the adjoining figure, DA = CB and AX = BY. Prove Z
that ∆ DAY ≅ ∆ CBX.
A X Y B
B

7. In ∆ ABC, ∠A = ∠C and BM bisects ∠ABC. Prove that BM
is perpendicular to AC.
A C
M
B
8. In the adjoining figure, O is the midpoint P
of PQ and ∠A = ∠B. Prove that O Q
∆ PAO ≅ ∆ QBO. A

K
9. In the adjoining figure, OD = OS and ∠K = ∠A. D
Prove that ∆ KOD ≅ ∆ AOS. O S
A
R T B S
10. In the given figure, ∆ PQR ≅ ∆ TSI and RA, IB are
their respective medians. Prove that RA = IB. Q
P A I

AT A GLANCE
¾ Two figures are said to be congruent if they have same shape and size.
¾ Two line segments are said to be congruent iff they have the same length, i.e., AB ≅ CD if and
only if AB = CD.
¾ Two angles are said to be congruent if and only if ∠ABC ≅ ∠DEF.
¾ Proving the congruency of plane figures by placing trace copy or cut-out of one figure on the
other is known as the method of superposition. We say that two figures are congruent if they
cover each other exactly, i.e., they are coincident.

Criterion of congruency
of triangles Explanation

Two triangles are congruent, if three sides of one triangle are
SSS
equal to the corresponding three sides of the other triangle.

Two triangles are congruent, if two sides and the included angle
SAS of one triangle are equal to the corresponding two sides and
the included angle of the other triangle.

Two triangles are congruent, if two angles and the included
ASA side of one triangle are equal to the corresponding two angles
and the included side of the other triangle.
Two right triangles are congruent, if the hypotenuse and any one
RHS side of one triangle are equal to the corresponding hypotenuse
and any one side of the other triangle.

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