In Exercises 17 to 24, complete each proof.
Given:
Prove:
PROOF | |
Statements | Reasons |
1.
2. 3. ? 4. 5. 6. ? |
1. ? 2. If 2 || lines are cut by a transversal, corresponding 3. Given 4. ? 5. ? 6. ? |
To prove:
The statement
Definition:
AA:
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
CSSTP:
Corresponding sides of similar triangles are proportional.
Description:
Given that
The given figure is shown below.
Figure
From the given figure, it is observed that the sides AB and DC are parallel,
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Therefore,
From the given figure, it is also observed that the sides AC and DE are parallel,
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Therefore,
The above mentioned AA definition, the two triangles ACB and DEC are similar since the two angles of one triangle are congruent to two angles of another triangle. Hence,
From the definition of CSSTP, corresponding sides of similar triangles are proportional
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