Congruence of Line Segments and Angles

Q.

Fill in the blanks:

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Square	-	-	-
Rectangle	-	-	-
Rhombus	-	-	-
Equilateral Triangle	-	-	-
Regular Hexagon	-	-	-
Circle	-	-	-
Semi-circle	-	-	-

Q. Question 4
In figure, $BA\perp AC,DE\perp DF$ such that BA =DE and BF =EC. Show that $\Delta ABC\cong \Delta DEF$

Q.

Name the different types of polyhedral solids.

Q.

Choose the correct option from the given options.

1. a-ii b-iii c-i

2. a-iii b-i c-ii

3. a-iii b-ii c-i

4. a-i b-ii c-iii

Q.

Question 4
In $\Delta ABC,\angle A={30}^{\circ },\angle B={40}^{\circ }and\angle C={110}^{\circ }$
In $\Delta PQR,\angle P={30}^{\circ },\angle Q={40}^{\circ }and\angle R={110}^{\circ }$
A student says that $\Delta ABC\cong \Delta PQR$ by AAA congruence criterion. Is he justified? Why or why not?

Q.

How many right angles are there in a cubical room? [1 MARK]

Q. In the figure, the two triangles are congruent. The corresponding parts are marked. Complete the congruent statement $\Delta RAT\cong$ [1 MARK]

Q. Question 8
In the figure, $l\parallel m$ and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points of l and m, respectively.

Q.

What type of triangle has three congruent sides?

1. Isosceles triangle

2. Equilateral triangle

3. Scalene triangle

Q. In which of the following figures, the sides are always congruent line segments?

1. Rhombus
2. Square
3. Equiangular triangle
4. All of the above.

Q.

Prove that in the following kite, $\Delta ADC$ is congruent to $\Delta ABC$. Given that AD = AB and $\angle ADC$ = $\angle ABC$ = ${90}^{\circ }$
[2 MARKS]

Q. Question 3
ABC is an isosceles triangle with AB = AC and D is a point on BC such that $AD\perp BC$ (see figure). To prove that $\angle BAD=\angle CAD$, a student proceeded as follows.

In $\Delta ABD$ and $\Delta ACD$, we have AB= AC [given]
$\angle B=\angle C$ [because AB=AC]
And $\angle ADB=\angle ADC$
Therefore, $\Delta ABD\cong \Delta ACD$ [by AAS congruence rule]
So, $\angle BAD=\angle CAD$ [by CPCT]
What is the defect in the above arguments?

Q. The interior angles of a square are ________ .

1. concurrent
2. not concurrent
3. congruent
4. not congruent

Q. In Triangle ABC If $\angle B$ and in Triangle PQR $\angle Q$ are acute angles such that $\sin B=\sin Q$ then prove that $\angle B=\angle Q$

Q.

Question 150 (i)

In the given figure, PQ = PS and $\angle 1=\angle 2$
Is $\Delta PQR\cong \Delta PSR$? Give reason.

Q.

Which transformation does not belong with the other three? Explain your reasoning.

Q. (a) Observe the given triangles and explain, why is $\Delta ABC\cong \Delta FED$?



(b) In a $\Delta$ABC, $\angle$B = 50${}^{\circ }$ and $\angle$C is 60${}^{\circ }$. Find $\angle$A.
[4 MARKS]

Q.

Given is a quadrilateral ABCD in which $\Delta ADC\cong \Delta ABC$. Which congruency criteria is used?

1. ASA

2. SAS

3. SSA

4. SSS

Q.

For constructing $\Delta$LMN exactly identical to $\Delta$ABC, choose from the options, the measurements required.

1. LM, MN, LN, ∠MLN and ∠MNL

2. MN and LN

3. LM, MN, LN and ∠MLN

4. LM, MN and LN

Q. In Fig $6.9$, $\angle 1=\angle 2$ and $\Delta NSQz\Delta MTR$, then prove that $\Delta PTS-\Delta PRQ$

Q. Construct a circle of radius 7 cm. In that circle, draw two congruent angles of any degree. [3 Marks]

Q.

Question 79(i)

In the given figure P, Q and R are collinear points and TQ $\perp$ PR.
Pair of complementary angles.

Q.

Give the name of the angle which is made up of less than $\frac{1}{4}$ of a revolution.

Q.

Tell whether the blue figure is a translation, reflection, rotation, or dilation of the red figure.

Q. The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.

Point	A	B	C	D	E
Co-ordinate	-3	5	2	-7	9

1. seg DE and seg AB
2. seg BC and seg AD
3. seg BE and seg AD
4. none of above

Q. Given $\angle ABC$ is congruent to $\angle PQR$. Then which of the following statements is true?

1. All of the above
2. $BC=QR$
3. $m\angle ABC=m\angle PQR$
4. $AB=PQ$

Q. Find the value of x of y using the information shown in the figure. Find the measure of $\angle ABD$ and $\angle ACD$

Q.

Tell whether the blue figure is a translation, reflection, rotation, or dilation of the red figure.

Q. An equilateral triangle is made up of ___ congruent line segments.

1. 3

Q. Line segment $AB$ is parallel to another line-segment $CD$, $O$ is the midpoint of $AD$.Show that $△AOB\cong △DOC$