Question 5

Check if the two figures are congruent.

Circle the pairs that appear congruent.

What measurements would you take to create a figure congruent to a given:

(a) Circle

(b) Rectangle

Using this, state how would you check if two —

(a) Circles are congruent?

(b) Rectangles are congruent?

Suppose $\Delta \text{HEN}$ is congruent to $\Delta \text{BIG}$. List all the other correct ways of expressing this congruence.

Determine whether the triangles are congruent. If yes, express the congruence.

In the figure below, $AB = AD$, $CB = CD$.

Can you identify any pair of congruent triangles? If yes, explain why they are congruent.

Does $AC$ divide $\angle BAD$ and $\angle BCD$ into two equal parts? Give reasons.

In the figure below, are $\triangle DFE$ and $\triangle GED$ congruent to each other? It is given that $DF = DG$ and $FE = GE$.

Identify whether the triangles below are congruent. What conditions did you use to establish their congruence? Express the congruence.

Given that $CD$ and $AB$ are parallel, and $AB = CD$, what are the other equal parts in this figure? (Hint: When the lines are parallel, the alternate angles are equal. Are the two resulting triangles congruent? If so, express the congruence.)

Given that $\angle ABC = \angle DBC$ and $\angle ACB = \angle DCB$, show that $\angle BAC = \angle BDC$. Are the two triangles congruent?

Identify the equal parts in the following figure, given that $\angle ABD = \angle DCA$ and $\angle ACB = \angle DBC$.

$\Delta \text{AIR} \cong \Delta \text{FLY}$. Identify the corresponding vertices, sides and angles.

Each of the following cases contains certain measurements taken from two triangles. Identify the pairs in which the triangles are congruent to each other, with reason. Express the congruence whenever they are congruent.

(a) $AB = DE$, $BC = EF$, $CA = DF$

(b) $AB = EF$, $\angle A = \angle E$, $AC = ED$

(c) $AB = DF$, $\angle B = \angle D = 90^\circ$, $AC = FE$

(d) $\angle A = \angle D$, $\angle B = \angle E$, $AC = DF$

(e) $AB = DF$, $\angle B = \angle F$, $AC = DE$

It is given that $OB = OC$, and $OA = OD$. Show that $AB$ is parallel to $CD$.
[Hint: $AD$ is a transversal for these two lines. Are there any equal alternate angles?]

$\text{ABCD}$ is a square. Show that $\Delta \text{ABC} \cong \Delta \text{ADC}$. Is $\Delta \text{ABC}$ also congruent to $\Delta \text{CDA}$?

Give more examples of two triangles where one triangle is congruent to the other in two different ways, as in the case above. Can you give an example of two triangles where one is congruent to the other in six different ways?

Find $\angle B$ and $\angle C$, if $A$ is the centre of the circle.

Find the missing angles. As per the convention that we have been following, all line segments marked with a single '|' are equal to each other and those marked with a double '|' are equal to each other, etc.