Question

Prove the following statement using the given pieces of information.2Given: ZGPS = ZJPS, PS_L_GJProve: ASJP – ASGPZGPS ZJPSbecause perpendicular lines form right angles, and all right anglès are congruent.PS and PS arethe two pairs of congruent angles.Click to select your answer(s).

Answer 1

Answer:

$\measuredangle GPS=\measuredangle JPS$

Because it is one of the given pieces of information.

$\measuredangle PSG\cong\measuredangle PSJ$

because perpendicular lines form right angles, and all right angles are congruent.

PS and PS are adjacent sides next to the two pairs of congruent angles.

$PS\cong PS$

By the Reflexive Property of Congruence

$\Delta SJP\cong\Delta SGP$

by ASA triangle congruence rule

Explanation:

Given the figure of the triangle in the attached image.

Given that;

$\measuredangle GPS=\measuredangle JPS$

Because it is one of the given pieces of information.

Then we can observe that;

$\measuredangle PSG\cong\measuredangle PSJ$

because perpendicular lines form right angles, and all right angles are congruent.

Also,

PS and PS are adjacent sides next to the two pairs of congruent angles.

And;

$PS\cong PS$

By the Reflexive Property of Congruence

Thus,

$\Delta SJP\cong\Delta SGP$

by ASA triangle congruence rule