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According to the third angle theorem, __________.


A.


if a triangle has two acute angles, then the third angle must also be acute

B.


if one angle of a triangle is congruent to another angle of the same triangle, then the third angle must also be congruent

C.


if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles is also congruent

D.


if the third angle of one triangle is congruent to the third angle of another triangle, then the two triangles are congruent

Verified Answer :

the answer is C it will be congruent to another angle

JeanaShupp

Answer: If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles is also congruent


Step-by-step explanation:

The third angle theorem says that if two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent. This is called the Third Angle Theorem.

Let ΔABC and ΔPQR are two triangles such that

∠A≅∠P and ∠B=∠Q.......(1)

Also ∠R=180°-(∠P+∠Q) [By angles sum property in  ΔPQR ]......(2)

∠C=180°-(∠A+∠B) [By angles sum property in ΔABC]

⇒∠C=180°-(∠P+∠Q)     [from (1)]

⇒∠C=∠R      [from (2)]

Hence proved.

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