The triangle ACB is similar to triangle DCE by the SSS similarity theorem. Option (a) is correct.
Further explanation:
The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.
There are many similarity rules and are as follows.
1. Angle AngleAngle (AAA)
2. Side SideSide (SSS)
3. Side Angle Side (SAS)
Given:
The options are as follows.
(a) The SSS similarity theorem
(b) The AA similarity postulate
(c) The HL similarity theorem
Explanation:
The length of side AC can be obtained as follows,
[tex]\begin{aligned}AC &= 6 + 3\\&=9\\\end{aligned}[/tex]
The length of side BC can be obtained as follows,
[tex]\begin{aligned}BC &=8 + 4\\&=12\\\end{aligned}[/tex]
The length of side AB is 15, length of side DE is 5, length of side DC is 3, and the length of side CE is 4.
If the triangle ACB is similar to triangle DCE then the sides are proportional.
The proportional of corresponding side can be obtained as follows,
[tex]\begin{aligned}\frac{{DE}}{{AB}}&= \frac{{DC}}{{AC}}=\frac{{CE}}{{CB}}\\\frac{5}{{15}}&=\frac{3}{9}=\frac{4}{{12}}\\\frac{1}{3}&=\frac{1}{3}=\frac{1}{3}\\\end{aligned}[/tex]
The corresponding sides are proportional. Therefore the triangles are similar.
The triangle ACB is similar to triangle DCE by the SSS similarity theorem. Option (a) is correct.
Kindly refer to the image attached.
Option (a) is correct
Option (b) is not correct
Option (c) is not correct
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Triangle
Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle.
