Question

Complete the proof by providing the missing statement and reasons

Answer 1

Answer:

In triangle SHD and triangle STD.

$\overline{SD} \perp \overline{HT}$          [Side]

Since, a line is said to be perpendicular to another line if the two lines intersect at a right angle.

⇒ $\angle SDH = \angle SDT = 90^{\circ}$

$\overline{SH} \cong \overline{ST}$       [leg]               [Given]

Reflexive property states that the value is equal to itself.

$\overline{SD} \cong \overline{SD}$       [Leg]       [Reflexive property]

HL(Hypotenuse-leg) theorem states that any two right triangles that have a congruent hypotenuse and a corresponding congruent leg are the congruent triangles.

then, by HL theorem;

$\triangle SHD \cong \triangle STD$                       Proved!