Question

1. Supply the missing reasons to complete the proof:

Answer 1

Answer:

(1) The triangle PQR and SRT are congruent by ASA postulate. The sides PR and SR are congruent by CPCTC.

(2) The angles SDH and SDT are right angles by definition of perpendicular line. SD=DS by reflexive property. Triangles SHD and STD are congruent by HL theorem.

Step-by-step explanation:

(1)

From the given information

$\angle Q\cong \angle T$

$QR\cong TR$

$\angle PRQ\cong \angle SRT$       (Vertical angles are congruent)

By ASA postulate the triangles PRQ and SRT are congruent.

$\triangle PRQ\cong \triangle \SRT$

According to CPCTC(corresponding parts of congruent triangles are congruent).

$PR\cong SR$

Therefore, the triangle PQR and SRT are congruent by ASA postulate. The sides PR and SR are congruent by CPCTC.

(2)

Given Information: SD⊥HT

$SH\cong ST$

According to the definition of perpendicular line, if a line intersects another line at right angle (90 degree), then the lines are perpendicular to each other.

Since the lines SD and HT are perpendicular lines therefore the angles between them is 90 degree.

The angle SDH and angle SDT are right angles.

$\angle SDH\cong \angle SDT=90^{\circ}$      (Rights angles)

$SH\cong ST$                                                    (Given)

$SD\cong SD$                                                   (Common side)

$SD\cong DS$                                                   (reflexive property)

If one leg and hypotenuse of two right angles are congruent, then these triangles are congruent to each other by HL postulate. So by HL theorem

$\triangle SHD\cong \triangle \STD$.