MATHS 3 Marks Question

Given DF = DG and FE = GE
The side DE is common to both triangles ∆DFE and ∆DGE
Hence, by the SSS congruence criterion
∆DFE ≅ ∆DGE
The order of the vertices matters in congruence statements.
The vertices must correspond correctly.
In ∆DFE and ∆DGE
DF corresponds to DG
FE corresponds to EG
ED is common.
Given statements DF = DG and FE = GE do not support the congruence of ∆DFE and ∆GED because the corresponding sides are not equal.

Given AD = AB
CB = CD
AC = AC (Common side)
Since all three sides of ∆ABC are equal to the corresponding three sides ∆ADC, the triangles are congruent by the side-side-side (SSS) congruence criterion.
Hence ∆ABC ≅ ∆ADC
Yes, AC divides ∠BAD and ∠BCD into equal parts.
Since ∆ABC ≅ ∆ADC
Then, ∠BAC = ∠DAC and ∠BCA = ∠DCA
This means that AC bisects both ∠BAD and ∠BCD.

(a) I will measure the radius or diameter of the given circle.
(b) I will measure the length and breadth of the given rectangle.
(a) I will place one circle over another circle.
If they exactly superimpose, they are congruent.
In this case, both will have the same radius.
(b) I will place one rectangle over another rectangle.
If they exactly superimpose, they are congruent.
In such a case, both will have the same length and breadth.

Here ∆AIR ≅ ∆FLY.
The corresponding parts are as follows:
Corresponding Vertices
A corresponds to F
I corresponds to L
R corresponds to Y
Corresponding Sides
AI corresponds to FL
IR corresponds to LY
AR corresponds to FY
Corresponding Angles
∠A corresponds to ∠F
∠I corresponds to ∠L
∠R corresponds to ∠Y