Question

a) Determine if the triangles are similar.b) If they are similar write the reason. (SSS, SAS, AA, NONE)c) The red segments are called...____(medians, heights, perpendicular bisectors, angle bisectors)d) ×=

Answer 1

• a. Yes

,

• b. SAS

,

• c. Height

,

• d. x=14

Step-by-step explanation:

Part A

The two triangles have an angle of 76 degrees at the altitudes U and F respectively.

Similarly, the ratio of their corresponding sides are:

`\begin{gathered} (WU)/(HF)=(9)/(21)=(3)/(7) \\ (UV)/(FG)=(18)/(42)=(3)/(7) \end{gathered}`

Part B

We conclude that:

Triangle HFG is similar to triangle WUV by the SAS congruence Theorem.

Part C

The red segments are called heights of the triangles.

Part D

The ratio of corresponding sides = 3/7

Thus:

`\begin{gathered} (6)/(x)=(3)/(7) \\ 3x=6*7 \\ x=(6*7)/(3) \\ x=14 \end{gathered}`