Question

1. in the figure to the right, bd//ae, bd measures 10 cm, ae measures 35 cm, and cd measures 14 cm. find the length of ce. the figure is not drawn to scale. a. 25 cm b. 39 cm c. 49 cm d. 21 cm 12. determine whether the two triangles are congruent. if they are, state by what theorem they are congruent. the triangles are not to scale. a. congruent by sas b. congruent by asa c. congruent by sss d. not congruent

Explanation:

11.

Step1: Use similar - triangle property

Since \(BD\parallel AE\), \(\triangle CBD\sim\triangle CAE\). Then \(\frac{BD}{AE}=\frac{CD}{CE}\).

Step2: Substitute the given values

We know that \(BD = 10\mathrm{cm}\), \(AE = 35\mathrm{cm}\), and \(CD = 14\mathrm{cm}\). Substituting into \(\frac{BD}{AE}=\frac{CD}{CE}\), we get \(\frac{10}{35}=\frac{14}{CE}\).

Step3: Cross - multiply and solve for \(CE\)

Cross - multiplying gives \(10\times CE=35\times14\). Then \(CE=\frac{35\times14}{10}=49\mathrm{cm}\).

The Side - Side - Side (SSS) congruence theorem states that if the three sides of one triangle are equal to the three corresponding sides of another triangle, the two triangles are congruent. Here, the side lengths of the two triangles are \(10\mathrm{m}\), \(15\mathrm{m}\), \(17\mathrm{m}\) in the same order, so the two triangles are congruent by SSS.

Answer:

c. 49 cm

12.