PART - 2 CH : 1 Geometric Twins MATHS - PART - 2 CH : 1 Geometric Twins

Circle the pairs that appear congruent.

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.)

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

Check if the two figures are congruent.

Find ∠B and ∠C, if A is the centre of the circle.

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?]

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.

ABCD is a square. Show that ∆ABC ≅ ∆ADC. Is ∆ABC also congruent to ∆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?

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
∠A = ∠E
AC = ED
(c) AB = DF
∠B = ∠D = 90°
AC = FE
(d) ∠A = ∠D
∠B = ∠E
AC = DF
(e) AB = DF
∠B = ∠F
AC = DE

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

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 ∠BAD and ∠BCD into two equal parts? Give reasons.

What measurements would you take to create a figure congruent to a given:
(a) Circle
(b) Rectangle
Using this, state how you would check if two
(a) Are circles congruent?
(b) Rectangles are congruent?

∆AIR ≅ ∆FLY. Identify the corresponding vertices, sides, and angles.