Matching wrong corresponding sides
"The Side Mismatch"
The Mistake in Action
Triangle ABC is similar to triangle PQR. AB = 4 cm, BC = 6 cm, PQ = 10 cm. Find QR.
Wrong: Scale factor = 10 ÷ 6 = 1.67, so QR = 4 × 1.67 = 6.67 cm
Why It Happens
Students pair up sides that look similar in length rather than sides in corresponding positions.
The Fix
In similar triangles, corresponding sides are opposite corresponding angles.
ABC ~ PQR means:
- A corresponds to P
- B corresponds to Q
- C corresponds to R
So AB corresponds to PQ (both opposite angle C/R). BC corresponds to QR (both opposite angle A/P).
Scale factor = $\frac{PQ}{AB} = \frac{10}{4} = 2.5$
QR = BC × 2.5 = 6 × 2.5 = 15 cm
Spot the Mistake
Can you identify where this student went wrong?
ABC ~ PQR, AB = 4, BC = 6, PQ = 10
SF = 10 ÷ 6 = 1.67
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: