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

`\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

Step-by-step 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