Question

deltamath
week 6: fri-th, similar word pb. due
wed for 100%
due: february 12 at 8:10 am
code: 8896
similar figures / proportion (level 2)
proving triangles similar
measure sides with a ruler and the
pythagorean theorem
measure sides with a ruler and the
pythagorean theorem
pythagorean theorem (honors)
pythagorean theorem (honors)
pythagorean theorem (honors)
scientific calculator
graphing calculator
note: this is
question
determine if triangle qrs and triangle tuv are or are not similar, and, if they are, state how you know.
(note that figures are not necessarily drawn to scale.)
answer
the triangles ~ similar.

Explanation:

Step1: Find ∠S in △QRS

First, calculate the missing angle in triangle QRS using the angle sum property of triangles (sum of angles = 180°).
$\angle S = 180^\circ - 79^\circ - 41^\circ = 60^\circ$

Step2: Check side ratios

Compare the ratios of corresponding sides around the congruent 41° angles.
$\frac{QR}{TU} = \frac{8}{16} = \frac{1}{2}$, $\frac{QS}{TV} = \frac{9}{18} = \frac{1}{2}$

Step3: Verify SAS similarity

Two sides are in proportion, and the included angle (41°) is congruent for both triangles. This satisfies the SAS (Side-Angle-Side) Similarity Criterion.

Answer:

The triangles are similar, by the SAS Similarity Criterion (the included angles of 41° are congruent, and the pairs of surrounding sides are in the same ratio of $\frac{1}{2}$).