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LekaFEV [45]
1 year ago
13

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

en 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.
Mathematics
1 answer:
givi [52]1 year ago
8 0
  1. 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. <2 ≅ <3 because of the corresponding angles theorem.
  3. <1 ≅ <4 because alternate angles are congruent if two parallel lines are cut by a transversal.
  4. <3 ≅ <4 by the substitution property of equality.
  5. AD/CD = EB/CB by the triangle proportionality theorem.
  6. If two angles in a triangle are congruent, the sides opposite the angles are congruent, so AE = EB.
  7. AD/CD = AB/CB by the substitution property of equality.

<h3>The properties of similar triangles.</h3>

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.

<h3>What is the substitution property of equality?</h3>

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: brainly.com/question/2459140

#SPJ1

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.

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Answer:

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Step-by-step explanation:

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From the question the points are

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The distance between them is

d =  \sqrt{ ({ - 8 - 3})^{2}  +  ({1 9 - 5})^{2} }  \\  =  \sqrt{( { - 11})^{2}  +  {14}^{2} }  \\  =  \sqrt{121 + 196}  \\  =  \sqrt{317}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 17.804493...

We have the final answer as

<h3>17.80 units to the nearest hundredth</h3>

Hope this helps you

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