Answer:
Explanation:
o show that the two triangles are similar, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.
The two triangles share a common angle at vertex E, which is congruent to angle DCE, since they are vertical angles. Additionally, angle CED is congruent to angle A because they are alternate interior angles formed by a transversal intersecting parallel lines.
To show that the corresponding sides are proportional, we can use the side-angle-side (SAS) similarity theorem. In particular, we can compare the ratio of the length of corresponding sides:
DE/EC = 8/4 = 2
ED/AC = 4/6 = 2/3
CD/AD = 3/5
Since the ratios are equal, we can write the similarity statement as:
Triangle ACD ~ Triangle CED
The theorem used is the side-angle-side (SAS) similarity theorem.
To show that the two triangles are similar, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.
The two triangles share a common angle at vertex P, which is congruent to angle QPR since they are vertical angles. Additionally, angle APR is congruent to angle URP because they are alternate interior angles formed by a transversal intersecting parallel lines.
To show that the corresponding sides are proportional, we can use the side-angle-side (SAS) similarity theorem. In particular, we can compare the ratio of the length of corresponding sides:
PR/AP = 12/4 = 3
UR/QA = 21/7 = 3
RU/PA = 12/4 = 3
Since the ratios are equal, we can write the similarity statement as:
Triangle APQ ~ Triangle PRU
The theorem used is the side-angle-side (SAS) similarity theorem.