MATHS 2 Marks Questions

Given the side lengths of the two triangles
RE = 3.5 cm, ED = 5 cm, RD = 6 cm
and JA = 3.5 cm, AM = 5 cm, JM = 6 cm
Clearly RE = JA = 3.5 cm
ED = AM = 5 cm
RD = JM = 6 cm
Hence ∆RED ≅ ∆JAM.

To check if the two figures are congruent, one would need to measure the lengths of the corresponding line segments and the angle between them.
Yes, each of the given figures is congruent. Length of line segments in each figure is 3.3 cm (Horizontal line) and 2.3 cm (Vertical line), and the angle between them is 82°.

In ∆BAC
AB = AC = Radius of the circle.
Let ∠ABC = ∠ACB = x (angles opposite to equal sides are equal)
Then, x + x + 120° = 180° (∵ Sum of all the angles in a triangle is 180°)
⇒ 2x = 180° – 120°
⇒ 2x = 60°
⇒ x = 30°
Hence ∠B = ∠C = 30°

Given OB = OC
OA = OD
Then ∠AOB = ∠COD
∆AOB ≅ ∆COD (∵ Side angle side condition)
So, these two triangles can be superimposed exactly.
Therefore, ∠A = ∠D
∠B = ∠C
Hence, AB is parallel to CD.

Given ∠ABD = ∠DCA; ∠ACB = ∠DBC
∠AOB = ∠DOC (∵ They are vertically opposite angles)
AO = DO; CO = BO
∆COD ≅ ∆BOA
Angle-side-angle condition

Let ∠ABC = a = ∠DBC
and let ∠ACB = b = ∠DCB
BC is a common side of the two triangles, then ∆ABC ≅ ∆DBC
Angle Side Angle Congruence:
When two triangles are congruent, their corresponding parts are equal [CPCT]
Since ∆ABC ≅ ∆DBC, their corresponding angles are equal.
Hence ∠BAC = ∠BDC

Here, BC = ZY = 5 cm
BA = ZX = 7 cm
∠ABC = ∠XZY = 47°
∆ABC ≅ ∆XZY
Since the two sides and the included angle of triangle ABC are equal to the two sides and the included angle of triangle XZY.
The triangles are congruent by the side-angle-side condition.
It can be expressed as ∆ABC ≅ ∆XZY.