Question

if PQ = DE , angle R = angle F , angle PQR = angle DEF , then the congruency rule is
(a) SSS
(b) SAS
(c) ASA
(d) AAS​

Answer 1

Answer:

(a) SSS

Explanation:

We will use the rule SSS

Because all the three sides are congruent(equal).

if PQ = DE

∠R = ∠F

so, ∠PQR = ∠DEF

So, the congruency rule will be SSS because SSS is used when all the sides are congruent to each other.

Hence, ∠PQR is equal to ∠DEF.

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Answer 2

Concept:

Triangle is a 2D surface having three sides and three angles, the sum of all angles of a triangle is 180°. And congruency rule is defined as the rule which is used to prove triangle congruent.

Given:

PQ = DE,

∠R = ∠F

∠PQR = ∠DEF

Find:

We are asked to find the congruency rule used in the triangle to prove them congruent.

Solution:

We have,

A triangle PQR and DEF,

∠R = ∠F

PQ = DE

∠PQR = ∠DEF

i.e. ΔPQR ≅ ΔDEF

Using the Angle Side Angle congruency rule,

i.e.

ASA congruency rule

Hence, the congruency rule used in the triangle is the ASA congruency rule.

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