Question

e. circle the figure that is congruent to the first figure. score /1
5in 7in 5in 7in 10in 14in 5in 7in
3in 5in 6in 3in
f. circle the figure that is similar to the first figure. score /1
8in 12in 8in 11in 4in 6in 4in 4in
100° 90° 100° 75°
10in 8in 5in 5in

Explanation:

Step1: Identify congruent triangles

Congruent triangles have identical side lengths. First triangle sides: 3 in, 5 in, 7 in. Compare to others:

• 2nd: 5 in, 5 in, 7 in (mismatch)
• 3rd: 6 in, 10 in, 14 in (mismatch)
• 4th: 3 in, 5 in, 7 in (match)

Step2: Identify similar triangles

Similar triangles have proportional sides and equal corresponding angles. First triangle: sides 8 in, 10 in, 12 in, included angle 100°. Check ratios and angle:

• 2nd: 90° angle (mismatch)
• 3rd: sides 4 in, 5 in, 6 in. Ratios: $\frac{4}{8}=\frac{1}{2}$, $\frac{5}{10}=\frac{1}{2}$, $\frac{6}{12}=\frac{1}{2}$; included angle 100° (match)
• 4th: 75° angle, unequal ratios (mismatch)

Answer:

E. The 4th triangle (with sides 3 in, 5 in, 7 in) is congruent to the first figure.
F. The 3rd triangle (with sides 4 in, 5 in, 6 in and 100° included angle) is similar to the first figure.