Question

Triangle abc is similar to triangle bcd . triangle abc and triangle bcd. the triangles share the same side, line segment bc. line segment ab is labeled nine point six centimeters. line segment bc is labeled six centimeters. part a what is the length of cd¯¯¯¯¯¯¯¯ ? responses a. 1.6 cm b. 3.6 cm c. 3.75 cm d. 4.0 cm

Answer 1

The length of line segment CD can be found using the proportions of the similar triangles ABC and BCD, resulting in a length of 3.75 cm.

Step-by-step explanation:

The question pertains to the concept of similar triangles where one side is shared (line segment BC) among them, and the side lengths of AB and BC are given, with AB being 9.6 cm long and BC being 6 cm long. Since triangle ABC is similar to triangle BCD and they share the side BC, their corresponding sides are proportional. To find the length of CD, we need to set up a proportion based on the side lengths of similar triangles.

Assuming that AB corresponds to CD in the smaller triangle ABC, and BC corresponds to itself because it's shared, the proportion can be set up as:

AB / BC = BC / CD

9.6 cm / 6 cm = 6 cm / CD

After cross-multiplication and solving for CD, we get:

CD = 6 cm * 6 cm / 9.6 cm

CD = 36 cm2 / 9.6 cm

CD = 3.75 cm

Therefore, the answer appears to be option c: 3.75 cm, as that is the length of line segment CD based on the proportions of the similar triangles.

Answer 2

So the answer is d) 4.0 cm.

Since triangles ABC and BCD are similar and share the side BC, you can use proportional sides to find the length of CD. Based on the information provided:

AB = 9.6 cm

BC = 6 cm (shared side)

Let CD be the unknown length. Since triangles are similar, the corresponding sides are proportional:

AB/BC = CD/BC

Substituting the known values:

9.6 cm / 6 cm = CD / 6 cm

Cross-multiplying:

9.6 cm * 6 cm = CD * 6 cm

Simplifying:

57.6 cm = 6 cm * CD

Dividing both sides by 6 cm:

CD = 9.6 cm

Therefore, the length of CD is 4.0 cm.