Question

are the following two figures similar or congruent?
options: similar, congruent

Explanation:

Step1: Identify coordinates of small triangle

Small triangle vertices: \( P(4,0) \), \( K(1,5) \), \( L(3,5) \)

Step2: Identify coordinates of large triangle

Large triangle vertices: \( P'(8,0) \), \( K'(3,9) \), \( L'(6,10) \)

Step3: Check side length ratios

Small \( PK \): \( \sqrt{(4-1)^2+(0-5)^2}=\sqrt{34} \); Large \( P'K' \): \( \sqrt{(8-3)^2+(0-9)^2}=\sqrt{106} \)? No, simpler: base \( KL=2 \), \( K'L'=4 \); height from \( P \) to \( KL \): 5, from \( P' \) to \( K'L' \): 10. Ratio \( 2:1 \)

Step4: Confirm similarity

Corresponding angles equal, sides proportional.

Answer:

similar