Question

prove that triangle PRQ congruent triangle TRS and state the rule and three pairs used to prove the triangle congruent is angle S = angle Q why​

Answer 1

Answer:

Side Congruence

 

Conditions for the SAS - Side Angle Side congruence

Two triangles are said to be congruent if two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

Experiment to prove Congruence with SAS:

∆LMN with LM – 8 cm, MN – 10 cm, ∠M – 60°

Also, draw another ∆XYZ with XY = 8cm, YZ = 10cm, ∠Y= 60°.

We see that LM = XY, AC = ∠M = ∠Y and MN = YZ



Make a trace copy of ∆XYZ and try to make it cover ∆LMN with X on L, Y on M and Z on N.

We observe that: two triangle cover each other exactly.

Therefore ∆LMN ≅  ∆XYZ

Worked-out problems on side angle side congruence triangles (SAS postulate):



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1. In the kite shown, PQ = PS and ∠QPR = ∠SPR.

(i) Find the third pair of corresponding parts to make ∆ PQR ≅ ∆PSR by SAS congruence condition.

(ii) Is ∠QRP = ∠SRP?

Solution:

(i) In ∆ PQR and ∆ PSR

PQ = PS                        →        given

∠QPR = ∠SPR                 →         given

PR = PR                        →         common

Therefore, ∆PQR ≅ ∆PSR by SAS congruence condition

(ii) Yes, ∠QRP = ∠SRP (corresponding parts of  congruence triangle).