Question

side lengths practice pages
study the example showing how to draw a triangle from given side lengths. then solve problems 1 - 7.
example
do the side lengths 3, 4, and 5 form a unique triangle or no triangle? support your reasoning with drawings.
you can compare the sum of the two shorter side lengths to the longest side length.
since 3 + 4>5, these side lengths can form a triangle.
when you know all three side lengths of a triangle, there is only one possible triangle you can make.
so, the side lengths 3, 4, and 5 form a unique triangle.
1 do the side lengths 6, 6, and 14 form a triangle? explain. support your explanation with drawings.
2 are the two triangles below the same? explain why or why not.
3 students want to make some triangular banners. which set of side lengths can the students use to make a triangular banner?
a 5 in., 5 in., 15 in.
b 12 in., 12 in., 24 in.
c 9 in., 9 in., 18 in.
d 18 in., 23 in., 23 in.

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Analyze problem 1

For side - lengths 6, 6, and 14, calculate the sum of the two shorter sides: $6 + 6=12$. Since $12<14$, these side - lengths do not form a triangle.

Step3: Analyze problem 2

The two triangles have side - lengths 5, 7, 9 and 5, 7, 9. By the SSS (Side - Side - Side) congruence criterion, if the three side - lengths of one triangle are equal to the three side - lengths of another triangle, the two triangles are the same.

Step4: Analyze problem 3

Option A:

For side - lengths 5, 5, 15, $5 + 5 = 10<15$, so it cannot form a triangle.

Option B:

For side - lengths 12, 12, 24, $12+12 = 24$, which does not satisfy the triangle - inequality theorem.

Option C:

For side - lengths 9, 9, 18, $9 + 9=18$, which does not satisfy the triangle - inequality theorem.

Option D:

For side - lengths 18, 23, 23, $18+23>23$, $23 + 23>18$, and $18+23>23$, so it can form a triangle.

Answer:

1. No. Because $6 + 6<14$, violating the triangle - inequality theorem.
2. Yes. Because they have the same three side - lengths (5, 7, 9), satisfying the SSS congruence criterion.
3. D. 18 in., 23 in., 23 in.