Triangle A B C is reflected across the line of reflection m to form triangle A prime B prime C prime. Triangle A prime B prime C
2 answers:
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Important details about isosceles triangle ABC:
- The median CD, which is drawn to the base AB, also acts as an altitude to that base in the isosceles triangle (CD⊥AB). This indicates that triangles ACD and BCD are congruent right triangles, each with hypotenuses AC and BC.
- In isosceles triangle ABC, the sides AB and BC are equal, meaning AC=BC.
- The base angles at AB are equal, m∠A=m∠B=30°.
1. Consider the right triangle ACD. The angle adjacent to side AD is 30°, which dictates that the hypotenuse AC is double the length of the opposite side CD relating to angle A.
AC=2CD.
2. Now, for right triangle BCD, the angle next to side BD is also 30°, so hypotenuse BC is twice the opposite leg CD linked to angle B.
BC=2CD.
3. To calculate the perimeters of triangles ACD, BCD, and ABC:
4. If the total of the perimeters of triangles ACD and BCD is 20 cm greater than the perimeter of triangle ABC, then
5. Given that AC=BC=2CD, the lengths of legs AC and BC of the isosceles triangles are 20 cm.
Answer: 20 cm.