Question

Compete the proof by providing the missing statement and reasons. given sd pependicular ht ; sh = st prove shd = std

Answer 1

Answer:

In $\triangle shd$ and $\triangle std$

$sd \perp ht$

By definition of perpendicular: Lines that are right angle to each other.

$\angle sdh \cong \angle sdt = 90^{\circ}$ [Right angle]

$sh \cong st$   [Hypotenuse side]       [Given]

Transitive property says that segment is congruent to itself.

$sd \cong sd$         [By transitive property]

HL theorem states that if the hypotenuse and one leg of right triangle are equal to the hypotenuse and one leg of the another right angle , then the two triangle are congruent.

then by HL theorem;

$\triangle shd \cong \triangle std$          proved!