Please help me 10 points

Question

asked Nov 13, 2019 199k views

1 Answer

NeilG · Answer 1 · 2019-11-16T15:53:50+0000

Let us prove that angle 1 is complementary to angle 3 step by step.

1. We have been given that angle 1 is complementary to angle 2.

2. Since we know that complementary angles add up to 90 degrees, therefore, by the definition of complementary
$m\angle 1+ m\angle 2=90^(o)$ .

3. We have been also given that line segment BD bisects
$\angle ADC$ .

4. By the definition of bisect
$\angle 2 \cong \angle 3$ .

5. Angles are congruent if their measures, in degrees, are equal, therefore, by angle congruence postulate
$m\angle 2=m\angle 3$ .

6.
$m\angle 1+ m\angle 2=90^(o)$

Upon substituting
$m\angle 2=m\angle 3$ in above equation we will get,

$m\angle 1+ m\angle 3=90^(o)$

Therefore, by substitution property of equality
$m\angle 1+ m\angle 3=90^(o)$ .

Hence, proven that angle 1 is complementary to angle 3.