Triangles

Topics in this chapter

• Triangle Properties and Classification
• Triangle Areas and Altitudes
• Proportionality and Thales Theorem
• Similarity Criteria and Proofs
• Similar Triangle Measurements and Applications
• Pythagorean Theorem and Applications

Cheat sheet

Practice questions

1. Question 1Q-5D6ADD

   If in two triangles, $ABC$ and $PQR$, $\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$, then which of the following is correct?

   1. A.$\triangle PQR \sim \triangle CAB$
   2. B.$\triangle PQR \sim \triangle ABC$
   3. C.$\triangle CBA \sim \triangle PQR$
   4. D.$\triangle BCA \sim \triangle PQR$
   See the answer and solution
2. Question 2Q-4DB354

   In a $\triangle ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE \parallel BC$. If $AD = 2$ cm, $DB = 3$ cm, and $BC = 7.5$ cm, find the length of $DE$.

   1. A.$2.5$ cm
   2. B.$3$ cm
   3. C.$4.5$ cm
   4. D.$5$ cm
   See the answer and solution
3. Question 3Q-1AF308

   If $\triangle ABC \sim \triangle PQR$, with $\frac{\text{Area}(\triangle ABC)}{\text{Area}(\triangle PQR)} = \frac{9}{16}$ and $BC = 4.5$ cm, then the length of $QR$ is:

   1. A.$6$ cm
   2. B.$5.33$ cm
   3. C.$8$ cm
   4. D.$3$ cm
   See the answer and solution
4. Question 4Q-F66502

   ABC is an isosceles triangle right-angled at C. Prove that $AB^2 = 2AC^2$.

   See the answer and solution
5. Question 5Q-28A7E4

   Vertical heights of two similar triangles are $6$ cm and $9$ cm respectively. If the perimeter of the first triangle is $36$ cm, find the perimeter of the second triangle.

   1. A.$54$ cm
   2. B.$48$ cm
   3. C.$24$ cm
   4. D.$81$ cm
   See the answer and solution