MN=8.3 mm, mㄥP=42⁰

In ΔPQR and ΔXYZ,
RP = ZX, ㄥPRQ = ㄥXZY, RQ = ZY      [given]
i.e. rwo sides and the angle included berween them of ΔPQR are equal to rwo corresponding sides and the
angle included them of ΔXYZ.
So, ΔPRQ ≅ ΔXYZ          [by SAS congruence rule]

In ΔBCA and ΔDCA,
ㄥB= ㄥD =90°
Hypotenuse CA = Hypotenuse CA         [common]
BA = DA = 3.6 cm
Therefore, by RHS congruence rule, two triangles are congruent. The correspondence is B ↔️ D, A ↔️ A,
C ↔️ C.
In symbolic form, ΔBAC ≅ ΔDAC

Hence, the side included between ㄥM and ㄥN of ΔMNP is MN.

\(\bar { EF } \leftrightarrow \bar { QR } \).

We know that, in two triangles, if three angles of one triangle are respectively equal to three angles of the other triangle, then the triangles are not necessarily congruent.

e.g. Draw a ΔABC with ㄥA = 30°, ㄥB = 40°, ㄥC = 110°, BC = 2.0 cm [say] and draw other ΔPQR with ㄥP = 30°, ㄥQ = 40°, ㄥR = 110° and QR = 3.0 cm.
Clearly, these triangles have their corresponding angles equal but they are not congruent, because BC≠ QR. Hence, a student is not justified.

\(m\angle GBH=94°\)

(i) The three pairs of equal parts in ΔCBD and ΔBCE are
ㄥBDC = ㄥBEC = 90° [given]
CB = BC    [common]
BD = CE      [given]
(ii) Yes, In ΔCBD and ΔBCE, we have
ㄥBDC = ㄥBEC = 90° [given]
CB = BC [common]
BD = CE [given]
Therefore, by RHS congruence rule, two triangles are congruent. The correspondence is B H C, E HD,
C ↔️ B.
In symbolic form, ΔCBD ≅ ΔBCE.
(iii) Yes, here ΔCBD ≅ ΔBCE
We know that, the corresponding parts of two congruent triangles are equal.
Therefore, ㄥDCB = ㄥEBC.

We know that, if the hypotenuse and one side of a right angled triangle are respectively equal to the hypotenuse and one side of other right angled triangle, then the triangles are congruent by RHS congruence rule.
Here, we have to established by RHS congruence rule that
ΔABC ≅ ΔRPQ
Given, ㄥB = ㄥP = 90°
AB=RP

So, the required information needed is
Hypotenuse AC = Hypotenuse RQ

(i) Two line segments are congruent, if they have same length.
(ii) Among two congruent angles, one has a measure of 70°, i.ie measure of the other angle is 70°.
(iii) When we write ㄥA = ㄥB, we actually mean mㄥA = mㄥB.

In some special cases (which depend on the lengths of the sides and the size of the angle involved), SSA is enough to show congruence. However, it is not always enough.
Consider the following triangles :

Here side AB is congruent to side DE (S) side AC is congruent to side DF (S) angle C is congruent to angle F (A)
But the triangles are not congruent, as we can see.
What happens is this : If we draw a vertical line through point A in the first triangle, we can sort of "flip" side AB around this line to get the second triangle, If we were to lay one triangle on top of the other and draw the vertical line, this how it would look.

Clearly, side DE is just side AB flipped around the line. So, we have not changed the length of the side, and the other side AC (or DF) is unchanged, as is angle C (or F). So, these two triangles that have the same SSA information, but they are not congruent.

Not congruent