CBSE Questions for Class 7 Maths Congruence Of Triangles Quiz 3 - MCQExams.com

In right triangle $$ABC$$, right-angled at $$C, M$$ is the mid-point of hypotenuse $$AB.\ C$$ is joined to $$M$$ and produced to a point $$D$$ such that $$DM = CM$$. Point $$D$$ is joined to point $$B$$.Which of the following is correct.  
1144236_d943c20d343e45a98669109314fa1736.png
  • $$ \Delta \mathrm { AMC } \cong \Delta \mathrm { BMD } $$
  • $$ \angle D B C $$ is a right angle.
  • $$ \Delta D B C \equiv \Delta A BC $$
  • $$ \mathrm { CM } = \dfrac { 1 } { 2 } \mathrm { AB } $$
If two legs of a right triangle are equal to two legs of another right triangle. then the right triangles are congruent.
  • True
  • False
If two sides and one angle of a triangle are equal to the two sides and angle of another triangle, then the two triangles are congruent.
  • True
  • False
In Figure 6.28, two triangles are congruent by RHS.
1790305_848ca0c422384ee4baef0001b367d101.png
  • True
  • False
If two triangles are congruent, then the corresponding angles are equal.
  • True
  • False
If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent.
  • True
  • False
If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
  • True
  • False
In the above figure, if OA $$=$$ OB, OD $$=$$ OC then $$\Delta AOD \cong  \Delta BOC$$ by congruence rule :

84875_a19f92b5737c40a7b69b7eda2bfed6bb.png
  • $$SSS$$
  • $$ASA$$
  • $$SAS$$
  • $$RHS$$
State true/false:
If in $$\bigtriangleup ABC and \bigtriangleup QRP, AB =QR,\angle B=\angle R\:and \: \angle C=\angle P.$$ 
Then, by A.S.A criteria, $$\triangle ABC$$ and $$\triangle QRP$$ are congruent.
  • True
  • False
If in two triangles $$\Delta ABC$$ and $$\Delta PQR$$, $$AB = QR, BC = PR$$ and $$CA = PQ,$$ then :
  • $$\Delta ABC\cong \Delta PQR$$
  • $$\Delta CBA\cong \Delta PRQ$$
  • $$\Delta BAC\cong \Delta RPQ$$
  • $$\Delta PQR\cong \Delta BCA$$
State whether the given statement is true or false:
In $$\displaystyle \bigtriangleup ABC$$ and $$\bigtriangleup DEF, AB=DE,BC=EF$$ and $$\angle B=\angle E$$. The triangles are congruent by $$SSS$$ test.
  • True
  • False
In figure, if $$AB=AC$$ and $$AP=AQ$$, then by which congruence criterion $$\Delta PBC \cong \Delta QCB$$?

85216_57077f0aac474168a5790232927a8e2a.png
  • $$SSS$$
  • $$ASA$$
  • $$SAS$$
  • $$RHS$$
If $$D$$ and $$E$$ are the mid-points of the sides $$AB$$ and $$AC$$ respectively of $$\triangle ABC$$. $$DE$$ is produced to $$F$$. To prove that $$CF$$ is equal and parallel to $$DA$$, we need an additional information which is:
  • $$\triangle DAE$$ = $$\triangle EFC$$
  • $$AE = EF$$
  • $$DE = EF$$
  • $$\triangle ADE = \triangle ECF$$
$$\Delta ABC$$ is congruent of $$\Delta DEF$$, if
  • $$AB \neq DE$$, $$AC = 6 = DF$$, $$\angle A = \angle D$$
  • $$AB  = DE$$, $$AC = DF$$, $$\angle B =\angle E$$
  • $$AB = DE$$, $$AC \neq DF$$, $$\angle C =\angle F$$
  • $$AB = DE$$, $$AC = DF$$, $$\angle C \neq \angle F$$
In the given figure, $$ AB= AC $$ and $$ \angle DBC= \angle ECB= 90^{\circ} $$, then $$ AD= AE $$ .


177253_34cb3a065e3f4e3da0b03b2761edc9c9.png
  • True
  • False
In $$\triangle ABC$$ and $$\triangle DEF$$, $$AB = FD$$ and $$\angle A = \angle D.$$ The two triangles will be congruent by $$SAS$$ axiom, if:
  • $$BC = EF$$
  • $$AC = DE$$
  • $$AC = EF $$
  • $$ BC = DE$$
In the given figure, $$ AB= AC $$ and $$ \angle DBC= \angle ECB= 90^{\circ} $$,then $$ BD= CE $$ .

177252_864117fb88454d17952ac0932c66b945.png
  • True
  • False
In triangle $$ ABC $$, bisector of angle $$ BAC $$ meets opposite side $$ BC $$ at point $$ D $$. If $$ AB=AC $$, then $$BD=CD.$$
  • True
  • False

By which congruency are the following pair of triangles congruent:

In $$\Delta\,ABC$$ and $$\Delta \,DEF$$, $$\angle\,B = \angle\,E = 90\,^{\circ}, AC = DF$$ and $$BC = EF.$$
  • RHS
  • SAS
  • AAA
  • SSS
In the figure $$\angle  ABC=135^{\circ},\angle ABX=90^{\circ} ,\angle XCD=55^{\circ}, \angle BCD=100^{\circ}$$,then determine whether $$\angle XBC$$ and $$\angle XCB$$ are congruent to each other.
182921.jpg
  • $$\angle XBC = 45^{\circ}, \angle XCB = 46{\circ}$$
  • $$\angle XBC = 45^{\circ}, \angle XCB = 45^{\circ}$$
  • $$\angle XBC = 45^{\circ}, \angle XCB = 60^{\circ}$$
  • $$\angle XBC = 45^{\circ}, \angle XCB = 25^{\circ}$$
From the following figure, we can say:  $$ AD= CE $$
State TRUE or FALSE

177278_0e883d43d9b245eb8620a95d438ccbd2.JPG
  • True
  • False
State true or false:

In the given figure, the diagonals $$AC$$ and $$BD$$ intersect at point $$O$$ . If $$OB =OD$$ and $$AB//DC$$, then
$$Area \left ( \bigtriangleup \: DOC \right )=Area \left ( \bigtriangleup \: AOB \right )$$.

187405_2c47fa78a66644df82cf66a5f223c81b.jpg
  • True
  • False
$$ ABC $$ and $$ DBC $$ are two isosceles triangle on the same side of $$ BC $$. Then, $$ \angle BDA=  \angle CDA $$.
  • True
  • False
State the property by which $$\Delta ADB\, \cong\, \Delta ADC$$ in the following figure.,
267059_258da681a2f64d9892ce351444f35000.png
  • SAS property
  • SSS property
  • RHS property
  • ASA property
$$l$$ and $$m$$ are two parallel lines intersected by another pair of parallel lines $$p$$ and $$q$$. Then:
243664.png
  • $$\triangle ABC\cong \triangle CDA$$.
  • $$\triangle ABC\cong \triangle ADC$$.
  • $$\triangle ABC\cong \triangle DCA$$.
  • $$\triangle ABC\cong \triangle CAD$$.
If in two triangles $$PQR$$ and $$DEF$$, $$PR=\,EF$$, $$QR=\,DE$$ and $$PQ=\,FD$$, then  $$\triangle PQR\cong$$ $$\triangle$$ ___.
  • $$FDE$$
  • $$DEF$$
  • $$FED$$
  • $$DFE$$
Ankita wants to prove $$\Delta ABC\cong \Delta DEF$$ using $$SAS$$. She knows $$AB=DE$$ and $$AC=DF$$. What additional piece of information does she need?
  • $$\;\angle A=\angle D$$
  • $$\;\angle C=\angle F$$
  • $$\;\angle B=\angle E$$
  • $$\;\angle A=\angle B$$
By which congruency property, the two triangles connected by the following figure are congruent.
267009_3080971014a146b4b57e95ef180e1d16.png
  • SAS property
  • SSS property
  • RHS property
  • ASA property
In the given fig. if AD = BC and AD || BC, then:
267088_e939c7d8fbed4b92b71cbe272c58bdc9.png
  • AB = AD
  • AB = DC
  • BC = CD
  • None
ABC is an isosceles triangle in which the altitudes $$BE$$ and $$CF$$ are drawn to the equal sides $$AC$$ and $$AB$$ respectively. Then
245593_2ff3647a85154e409292466b46937894.png
  • $$BE = CF$$
  • $$BE = AB$$
  • $$AB = BC$$
  • $$AC = BC$$
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