1. supply the missing reasons to complete the proof: given: angle q is congruent to angle t and line qr is congruent to line tr prove: line pr is congruent to line sr my answers: 1. given 2. vertical angles 3. asa 4. cpctc 2. complete the proof by providing the missing statement and reasons. given: sd-ht; sh=st prove: shd=std my answers: 1. given 2. definition of perpendicular line 3. given 4. sd=ds 5. hl theorem

(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

      (Vertical angles are congruent)

By ASA postulate the triangles PRQ and SRT are congruent.

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

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

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.

     (Rights angles)

                                                   (Given)

                                                  (Common side)

                                                  (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

.

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are