1. Student’s Task11..22
Name:............................ Date: ............................
Mathematical Modeling
Using a ruler and a protractor,
• draw ΔDEF with ∠ D = 35°, ∠ F = 80°, and DF = 4cm
• draw ΔTRS with ∠ T = 35°, ∠ S = 80°, and ST = 7cm
• measure the lengths of EF, ED, RS, and RT
• determine the proportions of FD
,
EF
ST RS
and
ED
.
RT
Write down the results that you have obtained in the following table.
Side lengths of
ΔDEF
Side lengths of
ΔRST
Ratio Value
EF ED RS RT
FD
ST
EF
RS
ED
RT
Are ΔDEF and ΔTRS similar?
Do the results above demonstrate this: if in two triangles the corresponding
angles are the same size, then their corresponding sides are proportional?
What does this mean?
Mathematics for Junior High School Grade 9 / 3

2. Use a ruler and a protractor.
• Draw triangle ABC with AB = 8 cm, BC = 6 cm, and AC = 7
cm.
• Draw triangle PQR with PQ = 4 cm, QR = 3 cm, and PR = 3.5
cm.
• Measure ∠ A, ∠ B, ∠ C, ∠ P, ∠ Q, ∠ R.
• Is ∠ A = ∠ P, ∠ B = ∠ Q, ∠ C = ∠ R?
Are ΔABC and ΔPQR similar?
Do the results above demonstrate this: if in two triangles the
corresponding sides are proportional, their corresponding angles
are the same size?
What does this mean?
4 / Student’s Worksheet – Similarity and Congruency