2x-7=8x-47-(3x-14)/2
1 answer:
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Answer:
Part a) alternate interior angles theorem
Part b) vertical angles theorem
Part c) AA Similarity theorem
Part d) triangle ABC is similar with triangle EDC
Part e) The length side b is 3 cm
Step-by-step explanation:
Part a) we know that
The <u><em>Alternate Interior Angles Theorem</em></u> states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.
In this problem
The transversal is the segment BD and the parallel lines are AB and DE
so
----> by alternate interior angles theorem
Part b) we know that
<u><em>Vertical Angles Theorem</em></u> states that vertical angles are congruent. Vertical Angles are the angles opposite each other when two lines cross.
In this problem, the two lines that cross are BD and AE
so
----> by vertical angles theorem
Part c) we know that
The <u><em>AA Similarity Theorem</em></u> states: If two angles of one triangle are congruent to two corresponding angles of another triangle, then the triangles are similar
In this problem
triangle ABC is similar with triangle EDC by AA Similarity Theorem
Because
----> by alternate interior angles
----> by vertical angles
Part d) triangle ABC is similar with triangle EDC by AA Similarity Theorem
see the explanation Part c)
Part e) Find the length of side b
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
we have that
triangle ABC is similar with triangle EDC
so
Applying proportion
substitute the given values
solve for DC
therefore
The length side b is 3 cm