Two triangles are said to be congruent if they have similar properties. Thus the required options to complete the paragraph proof are:
a. angle 1 is congruent to angle 2.
b. alternate angles are congruent if two parallel lines are cut by a transversal.
c. [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]
The similarity property of two or more shapes implies that the shapes are congruent. Thus they have the same properties.
From the given diagram in the question, it can be deduced that
ΔABC ≅ ΔABE (substitution property of equality)
Given that EA is parallel to BD, then:
i. <2 ≅ <3 (corresponding angle property)
ii. <1 ≅ < 4 (alternate angle property)
Thus, the required options to complete the paragraph proof are:
- Angle 1 is congruent to angle 2.
- Alternate angles are congruent if two parallel lines are cut by a transversal.
- [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]
For more clarifications on the properties of congruent triangles, visit: https://brainly.com/question/1619927
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