EASY
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State by which rule of congruence is the pair of triangles congruent. (ASA/SSS/RHS)

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Important Questions on Congruence of Triangles

HARD
Let ABC be an acute angled triangle with AB=15 and BC=8. Let D be a point on AB such that BD=BC. Consider points E on AC such that DEB=BEC. If α denotes the product of all possible values of AE, find [α]10, whereα is the integer part of α.
MEDIUM
If ΔABCΔFED under the correspondence ABCFED, write all the Corresponding congruent parts of the triangles.
MEDIUM
Draw ABC and PQR such that they are equal in area but not congruent.
MEDIUM

In the given figure, AB=AD and CB=CD. Prove that ABCADC.

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MEDIUM

In the given figure, ABC is isosceles in which AB=AC. If E and F are the midpoints of AC and AB respectively. Prove that BE=CF.

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MEDIUM

In the given figure,PAAB, QBAB and PA=QB. Prove that OAPOBQ. Is OA=OB?

In the given figure, PA ⊥ AB, QB ⊥ AB and PA = QB. Prove that ΔOAP = ΔOBQ.  Is OA =OB? - Sarthaks eConnect | Largest Online Education Community

MEDIUM

In each pair of triangles below, find the pairs of matching angles and write them down.

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EASY
State the correspondence between the vertices, sides and angles if ABCEFD.
MEDIUM

In the given figure, triangles ABC and DCB are right-angled at A and D respectively and AC=DB. Prove that ABCDCB.

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EASY
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 then under what conditions will they be congruent?
MEDIUM

In the given figure, P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP=AQ. Prove that BQ=CP.

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MEDIUM

In the given figure, AD=BC and AD||BC. Is AB=DC? Give reasons in support of your answer.

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MEDIUM

In the given figure, ABC is an isosceles triangle in which AB=AC. Also, D is a point such that BD=CD. Prove that AD bisects A and D.

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HARD
Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.
EASY
If two triangles have their corresponding angles equal, are they always congruent? If not, draw two triangles which are not congruent but which have their corresponding angles equal.
MEDIUM

In the given figure, ABC is a triangle in which AD is the bisector of A. If ADBC, show that ABC is isosceles.

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EASY
If ABCXYZ and BAC=55o, then ZXY=?
HARD
In ΔABC, A=30o, B=40o and C=110o
In ΔPQR, P=30o, Q=40o and R=110o
A student says that ΔABCΔPQR by AAA congruence criterion. Is he justified? Why or why not?
MEDIUM

In the given figure, AB=AC and BD=DC. Prove ADB  ADC and hence show that ADB= ADC=90° and BAD=CAD.

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