Download Q1. State the conditions of congruence for the following

Q1.
State the conditions of congruence for the following:
(i)
line segment (ii) angles, (iii) squares, (iv) rectangles and (v) circles.
Q2.
Are two triangles congruent if two sides and an angle of one triangle are
respectively equal to two sides and an angle of the other? If not under what
conditions will be they congruent?
Q3.
Prove that the bisector of the vertical angle of an isosceles triangle bisects the
base at right angles.
Q4.
In the given figure,
and
such that
. Is
? Give reasons in support of your answer.
Q5.
In the given figure,
Q6.
In the given figure, triangles
and
Prove that
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. Prove that
are right angled at
.
respectively
.
Page 1 of 6
Q7.
In the given figure,
are two points on equal sides
isosceles triangle
Q8.
In the given figure,
produced to
Q9.
such that
. Prove that
of an
.
is an isosceles triangle in which
respectively such that
In the following figure,
be the mid points of
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. If
are
, prove that
is an isosceles triangle in which
respectively, prove that
.
. If
.
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Q10.
In the given figure
Q11.
If two squares have equal area, are they congruent? If two triangles have equal
area they congruent?
Q12.
Are two figures congruent if their area is equal? Are two circles congruent if they
have equal circumference?
Q13.
In the given figure,
such that
Q14.
bisect each other at
. Prove that
is an isosceles triangle in which
. Prove that
bisects
.
. Also
is a point
.
If the hypotenuse of a right triangle is equal to the hypotenuse of another right
triangle. Are the two triangles congruent?
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Page 3 of 6
Q15.
The sides
that
Q16.
have been produced such that
Q18.
. Prove
.
If
are equilateral triangles and
under which
Q17.
and
are congruent.
In the given figure if
In the given figure,
can you say about
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, state the condition(s)
, then find
is a rhombus, Are
.
are congruent? What
?
Page 4 of 6
Q19.
In the given figure,
is the mid point of
are equal in length. Prove that
Q20.
In the given figure
and
and perpendiculars
to sides
is an isosceles triangle.
. Prove that the triangles
are
congruent.
Answers
A1.
A2.
A3.
A4.
A5.
A6.
Hint: (i) same length (ii) same measurement (iii) same side length (iv) same
length and breadth (v) Same radius
No, Use SAS condition.
Hint: Prove that two triangles so formed are congruent.
Yes, By RHS condition of congruency.
Hint: Use SSS congruence condition.
Hint: Use RHS congruence condition.
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Page 5 of 6
A7.
Hint: Prove
A8.
Hint: Show that
A9.
Show that
A10.
Hint: Prove that
A11.
A12.
A13.
Yes, No
NO, Yes
Hint: Prove that congruency of triangles
A14.
A15.
A16.
A17.
No
Therefore, angle E = angle C, angle D = angle B. alternate angles are equal then
DE is parallel to BC
SSS, ASA, SAS
Hint:
A18.
Yes,
. By SAS congruence condition, CPCT.
are congruent.
then conclude.
are congruent. By SSS condition of congruency.
Also,
A19.
.
are congruent. By SSS condition of congruency.
Hint:
by CPCT.
A20.
Property of Isosceles triangle.
Hint: Use ASA congruence condition.
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