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This is one of our many quizzes on Quadrilateral congruence. Click on this to access more such competitive quizzes on Geometry.

Quadrilateral congruence Quiz 2

mathematics

 Suppose you want to show that two quadrilaterals are equal which of the following conditions can you use to do so?

 The sides of quadrilaterals can be equal even if the angles are not and the vice versa is also true. 

  Generally, you have to put sides and interior angles of one quadrilateral in correspondence with sides and angles of another and to prove that all corresponding pairs of sides and angles are congruent. $ \\ $ In the given options it is best if both the corresponding angles and sides are compared and equated, Hence option $(c)$ is correct.

 In the given figure it is known that the quadrilaterals PQRS and ABCD are congruent, what is the condition of congruence that they satisfy? $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/1836febd-ca90-4d43-952e-88d3ffc4929a1186365408511341614.png"/>

 Check the minimum condition required for the quadrilaterals to be congruent.

  In the given quadrilaterals $ABCD$ and $PQRS$ it is seen that $ \\ \angle B=\angle Q \\ BC=QR \\ \angle C=\angle R \\ \angle D=\angle S \\ AD=PS \\ $ So $ABCD\cong PQRS$ has ASAAS condition

 You were playing a puzzle with the rules that the final component has the angles in ratio $1:2:3:4$. You have to create the congruent quadrilateral in order to fix the puzzle. What are the angles you found in degrees?

 Consider the conditions of congruence of quadrilaterals. All the angles will be equal as the original figure.

Since he wishes to make the same quadrilateral so the new figure will be congruent, all the angles will be same in the new figure and hence using the property that sum of all angles of a quadrilateral is ${{360}^{\circ }}$. $ \\ $ Let the angles be $1x, 2x, 3x, 4x$ $ \\ 1x+2x+3x+4x=360 \\ 10x=360 \\ x=36 \\ 2x=72 \\ 3x=108 \\ 4x=114 \\ $

 Two quadrilaterals are as shown, by which property are they similar? $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/2e89cf72-1937-4bed-b308-523d9f604f862260444022945484238.png"/> 

 To make two figures that are equal in all the measurements, consider the conditions of congruence of quadrilaterals.

 On observing the given figures $ABCD$ and $PQRS$ we get, $ \\ PQ=AB \\ \angle P=\angle A \\ PS=AD \\ SR=CD \\ $ So the given figures are congruent using SSSAS

 Ramesh wishes to draw the quadrilateral that his teacher drew on board, but the angles are known to be $3x+10$, $5x+20$, $3x$ and $3x+6$. If the size of edges is given, find the largest angle of all. 

 All the angles will be equal as the original figure, use the angle sum property of the quadrilaterals to find the angles.

 Since he wishes to make the same quadrilateral so the new figure will be congruent, all the angles will be same in the new figure and hence using the property that sum of all angles of a quadrilateral is ${{360}^{\circ }}$. So $ \\ 3x+10+5x+20+3x+3x+6=360 \\ 14x+36=360 \\ 14x=360-36 \\ 14x=324 \\  x=\dfrac{324}{14}=23.14 \\ $ So the largest angle will be $5x+20=115.7+20={{135.7}^{\circ }}$