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kobusy [5.1K]
3 years ago
6

Match the following reasons with the statement givem

Mathematics
1 answer:
ANEK [815]3 years ago
7 0

Answer:

AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent

In triangle RAS and triangle QAT

\angle R =\angle Q   [Angle]

AS =AT    [Side]                                       [Given]

By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.

⇒ \angle 5= \angle 6      [By base ∠'s of isosceles triangle are equal]

By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.

\angle 4, \angle 5 are supplementary and \angle 6, \angle 7 are supplementary.

⇒\angle 4+ \angle 5 =180^{\circ} and

\angle 6+ \angle 7 =180^{\circ}  

Two \angle 's supplementary to equal \angle 's

\angle 4+ \angle 5 =\angle 6+ \angle 7

Since,  \angle 5 =\angle 6  

then, we get;

\angle 4 =\angle 7  [Angle]

then, by AAS postulates,

\triangle RAS \cong \triangle QAT

By CPCT[Corresponding Part of Congruent Triangles are equal]

RS = QT              Hence Proved!

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