Question

PLEASE HELP ME 100!!! POINTS A conjecture and the flowchart proof used to prove the conjecture are shown.

Given: m∠ABD=43°

m∠DBC=47°

Prove: △ABC is a right triangle.

Answer 1

Answer:

Add the two angles: 43° + 47° = 90°.

Step-by-step explanation:

A right triangle has an angle that equals 90°. Complementary angles equal 90°. Therefore, if you add these two angles, you will know whether or not △ABC is a right triangle. Triangle △ABC is broken up into two angles, m∠ABD and m∠DBC. When the measures m∠ABD and m∠DBC are added together, they equal 90°, and thus, form a complementary angle.

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer 2

Answer:

Givens

$m\angle ABD=43\°\\m\angle DBC=47\°$

To probe $\triangle ABC$ is a right triangle, we have to demonstrate that the vertex B holds a right angle, that is $m\angle ABC = 90\°$

Now, by sum of angles, we know

$m\angle ABC = m\angle ABD + m\angle DBC$

By given we know that

$m\angle ABD=43\°\\m\angle DBC=47\°$

Replacing these values, we have

$m\angle ABC = 43\°+ 47\°=90\°$

Then, $\angle ABC$ is a right angle by definition.

Finally, $\triangle ABC$ is a right triangle by definition, with right angle at vertex B.