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Triangles Practice 3: Applications, Proofs and Error Analysis

Section A: Applications

Question 1mcq
If △ABC∼△PQR\triangle ABC\sim\triangle PQR, AB=8AB=8 cm, PQ=12PQ=12 cm and BC=10BC=10 cm, find QRQR.
A.1212 cm
B.1515 cm
C.1616 cm
D.1818 cm
Question 2mcq
Two similar triangles have perimeters 3636 cm and 5454 cm. If a side of the smaller triangle is 88 cm, what is the corresponding side of the larger triangle?
A.1010 cm
B.1212 cm
C.1414 cm
D.1616 cm
Question 3mcq
A 1.51.5 m student casts a 22 m shadow. At the same time, a pole casts an 88 m shadow. What is the pole height?
A.44 m
B.55 m
C.66 m
D.88 m
Question 4mcq
A ramp forms a small triangle with rise 0.60.6 m and base 1.81.8 m. A similar larger ramp has base 4.54.5 m. What is its rise?
A.1.21.2 m
B.1.51.5 m
C.1.81.8 m
D.2.42.4 m
Question 5mcq
Which is the best first step in a structured similarity proof?
A.State the given information and what is to be proved.
B.Write the final answer only.
C.Assume all sides are equal.
D.Skip the diagram labels.

Section B: Proof and Misconception Checks

Question 6mcq
In a proof, after showing ∠A=∠P\angle A=\angle P and ∠B=∠Q\angle B=\angle Q, what should be written next?
A.△ABC∼△PQR\triangle ABC\sim\triangle PQR by AA similarity.
B.AB=PQAB=PQ because angles are equal.
C.△ABC≅△PQR\triangle ABC\cong\triangle PQR always.
D.AC=PRAC=PR without reason.
Question 7mcq
A student has △ABC∼△PQR\triangle ABC\sim\triangle PQR and writes AB/QR=BC/PQAB/QR=BC/PQ. What is the likely mistake?
A.Wrong correspondence of sides.
B.Using too many fractions.
C.Using the same unit.
D.Writing the triangles in order.
Question 8mcq
In a diagram, ABAB corresponds to DEDE, BCBC corresponds to EFEF, and ACAC corresponds to DFDF. Which ratio setup is correct?
A.AB/DE=BC/EF=AC/DFAB/DE=BC/EF=AC/DF
B.AB/EF=BC/DE=AC/DFAB/EF=BC/DE=AC/DF
C.AB/DF=BC/EF=AC/DEAB/DF=BC/EF=AC/DE
D.AB/BC=DE/DFAB/BC=DE/DF
Question 9mcq
If two similar triangles have area ratio 25:4925:49, what is the ratio of their corresponding sides?
A.5:75:7
B.25:4925:49
C.10:1410:14
D.7:57:5
Question 10mcq
In △ABC\triangle ABC, DE∥BCDE\parallel BC. If AD:DB=2:5AD:DB=2:5 and AC=21AC=21 cm, find AEAE.
A.55 cm
B.66 cm
C.77 cm
D.88 cm