In , side is extended to point E. When connected to vertex A, segment is parallel to segment . In this construction, you are given that bisects .

Prove:
Complete the paragraph proof.

A diagram of a triangle ABC. D is the midpoint of the base AC. A line connects BD. A dashed line AE and BE is drawn outside the triangle.

, since bisects and the two angles created on each side of the bisector at point B are equal. because of the corresponding angles theorem. because
. by the substitution property of equality. by the triangle proportionality theorem. If two angles in a triangle are congruent, the sides opposite the angles are congruent, so .
by the substitution property of equality.

Question

01-09-2022
Mathematics

Answered

In , side is extended to point E. When connected to vertex A, segment is parallel to segment . In this construction, you are given that bisects .

Prove:
Complete the paragraph proof.

A diagram of a triangle ABC. D is the midpoint of the base AC. A line connects BD. A dashed line AE and BE is drawn outside the triangle.

, since bisects and the two angles created on each side of the bisector at point B are equal. because of the corresponding angles theorem. because
. by the substitution property of equality. by the triangle proportionality theorem. If two angles in a triangle are congruent, the sides opposite the angles are congruent, so .
by the substitution property of equality.

Answer :

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Lanuel Lanuel · Answer 1 · 2022-09-04T02:59:53-04:00

Angle 1 is congruent to angle 2, since BD bisects <ABC and the two angles created on each side of the bisector at point B are equal.
<2 ≅ <3 because of the corresponding angles theorem.
<1 ≅ <4 because alternate angles are congruent if two parallel lines are cut by a transversal.
<3 ≅ <4 by the substitution property of equality.
AD/CD = EB/CB by the triangle proportionality theorem.
If two angles in a triangle are congruent, the sides opposite the angles are congruent, so AE = EB.
AD/CD = AB/CB by the substitution property of equality.

The properties of similar triangles.

In Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

What is the substitution property of equality?

The substitution property of equality states that assuming x, y, and z are three (3) quantities, and if x is equal to y (x = y) based on a rule and y is equal to z (y = z) by the same rule, then, x and z (x = y) are equal to each other by the same rule.

In this context, we can reasonably infer and logically deduce that the ratio of AD/CD is equal to AB/CB based on the substitution property of equality.

Read more on substitution property here: https://brainly.com/question/2459140

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Complete Question:

In ΔABC, side BC is extended to point E. When connected to vertex A, segment EA is parallel to segment BD. In this construction, you are given that BD bisects <ABC.

Prove: AD/CD = AB/CB.

Complete the paragraph proof.