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SashulF [63]
1 year ago
15

In ABC, 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

Mathematics
1 answer:
Anuta_ua [19.1K]1 year ago
6 0

Two triangles are said to be <u>congruent</u> if they have <em>similar</em> properties. Thus the required <u>options</u> to complete the <em>paragraph proof</em> are:

a. angle 1 is <u>congruent</u> to angle 2.

b. <em>alternate</em> angles are <u>congruent</u> if two parallel lines are cut by a <em>transversal</em>.

c. \frac{AD}{CD} = \frac{AB}{CB}

The <em>similarity property</em> of two or more shapes implies that the <u>shapes</u> are congruent. Thus they have the <em>same</em> properties.

From the given <u>diagram</u> in the question, it can be deduced that

ΔABC ≅ ΔABE (<em>substitution</em> property of equality)

Given that EA is <u>parallel</u> to BD, then:

i. <2 ≅ <3 (<em>corresponding</em> angle property)

ii. <1 ≅ < 4 (<em>alternate</em> angle property)

Thus, the required options to complete the <em>paragraph proof</em> are:

  • Angle 1 is <em>congruent</em> to angle 2.
  • Alternate angles are <u>congruent</u> if two parallel lines are cut by a <em>transversal</em>.
  • \frac{AD}{CD} = \frac{AB}{CB}

For more clarifications on the properties of congruent triangles, visit: brainly.com/question/1619927

#SPJ1

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