Question

question 13
two triangles have the same angle measures, but different side lengths. what does this tell us about the triangles?
they are similar but not congruent.
they are reflections of each other.
they are congruent.
they have no relationship.
question 14
a right triangle has legs of 5 and 12 units. what is the length of the hypotenuse?
10

Explanation:

Question 13

Similar triangles have equal - angle measures, and congruent triangles have equal - angle measures and equal - side lengths. Since side lengths are different here, they are similar but not congruent.

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 5\) and \(b = 12\).
\[c^{2}=5^{2}+12^{2}\]

Step2: Calculate \(a^{2}+b^{2}\)

\[5^{2}=25\], \[12^{2}=144\], so \(c^{2}=25 + 144=169\).

Step3: Find \(c\)

Take the square root of \(c^{2}\). Since \(c>0\), \(c=\sqrt{169}=13\).

Answer:

They are similar but not congruent.

Question 14