Question

6) Choose which postulate proves the triangles congruent.

Answer 1

Answer:

SAS(Side.Angle.Side

Step-by-step explanation:

since x is mid point of pr and qs so px=xr and x is midpoint of qs so qx=sx,

and two lines intercept so angles made on point x are equal.....hence 2 sides and one angle proved so triangles are equal

Answer 2

The postulate that can be used to prove that triangle QXP and triangle SXR are congruent to each other is: SAS Congruence Theorem,

Recall:

• Two triangles are congruent by the Side-Angle-Side Congruence Theorem, if two sides and one included angle of one triangle are congruent to two sides and the corresponding included angle in the other triangle.

Since X is a midpoint of QS and RP, therefore:

$PX \cong RX\\\\QX \cong SX$

• Also,

<PXQ = <SXR (vertical angles are congruent)

• Thus, triangle QXP and triangle SXR are congruent by SAS.

Therefore, the postulate that can be used to prove that triangle QXP and triangle SXR are congruent to each other is: SAS Congruence Theorem,

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