Year 11 Maths - Specialist
Geometry in the plane and proof
Proofs involving similarity
ACCOUNT REQUIRED
Unlock all 5 questions & worked solutions
You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.
All Questions
Access the full question set for every topic.
Worked Solutions
Step-by-step explanations for every answer.
Track Progress
Mark questions right or wrong and monitor your growth.
It's Free
No credit card required - sign up in under a minute.
Questions
Question 1
58305
The diagram shows the \(\Delta PQR\). \(ST\) is parallel to \(QR\). \(PT=6,\,TR=4\) and \(PQ=12\)
i) Prove that \(\Delta PST\) is similar to \(\Delta PQR\)
ii) Find the length of \(SQ\)
| $$ \begin{align} &\begin{aligned}\text{(i)}\quad \text{In} \triangle 'S PST,& PQR\\ \angle SPT&=\angle OPR \quad( \text{cummon}\ \angle)\\ \angle PST&=\angle PQR\\ (\text{corresponding}\ \angle\ \text{is} &= \text{In}\ ||\ \text{lines}\ ST,\ Q R)\\ \therefore \triangle P S T &||\ \triangle P Q R\ \text{(equianguler)}\end{aligned}\\ &\begin{aligned}\text{(ii)}\quad \text{Let}\ SQ&=x \rightarrow PS=12-x\\ \text{(corresponding}& \text{sides in the same ratio)}\\ \frac{P S}{P T} &=\frac{P \varphi}{P R} \\ \frac{12-x}{6} &=\frac{12}{10} \\ 120-10 x &=72 \\ 10 x &=48 \\ x &=4 .8 \end{aligned} \end{align} $$ |
|
📚 Want More Questions?
There are 4 more questions available. Create your free account to access the complete question set with detailed solutions.