Question

2. A sculptor is planning to make two triangular prisms out of steel. The sculptor will use ΔABC for the bases of one prism and ΔDEF for the bases of the other prism.
(a) Is ΔABC similar to ΔDEF ? Explain, and show your work. If you are showing that these triangles are similar you need to show which angles are congruent and show that the sides are proportional (3 points). Do not just say “yes” you will not receive credit. Please also state the similarity theorem or postulate you use (2 points)
(b) Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume (1 point)? How many times greater (1 point)? Show your work (3 points).

Answer 1

Answer:

a) SAS

b) Volume of DEF is 4 times the Volume of ABC

Step-by-step explanation:

a) since they have one same/congruent angle (angle B and angle E) and other two sides are in the same ratio, they are similar by SAS similarity theorem.

40/20 = 30/15 = 2

Therefore Δ ABC is similar to Δ DEF

b) Volume of a prism

= base area × height

Let height be 'h cm'

With Base ABC:

Volume = ½×20×15×h = 150h cm³

With Base DEF:

Volume = ½×40×30×h = 600h cm³

600h/150h = 4

Prism with base DEF has a greater volume; it's 4 times of the volume of the prism with base ABC