Question 8(Multiple Choice Worth 1 points)

Question

(03.05 MC)

ΔAXY is similar to ΔABC.

triangles ABC and AXY that share vertex A where point X is between points A and B and point Y is between points A and C

Which of the following expressions could be used to determine the length of segment AC?

AC = AB
AC = AY
AC equals AB times AY over AX
AC equals AB times AX over AY
Question 9(Multiple Choice Worth 1 points)
(03.05 MC)

An aerial camera is suspended from a blimp positioned at point D. It hangs at an altitude of 125 meters. If the camera hangs 10 meters below the blimp and the blimp attachment is 20 meters in length, how much ground distance from A to C can the aerial camera cover?

A blimp over triangle EDF with height of 10 meters and FE equals 20 meters and triangle ADC with height of 125 meters and ground distance AC. Triangles share point D.

62.5 m
125 m
250 m
500 m
Question 10(Multiple Choice Worth 1 points)
(03.05 MC)

triangle ADC with median DB where point B is between points A and C, AD equals 15, and DC equals 15

segment DB is an angle bisector of ∠ADC. Which statement best describes the relationship between the triangle ABD and CBD?

Triangles ABD and CBD are congruent by the SSS Congruence Postulate.
Triangles ABD and CBD are similar by the SSS Similarity Postulate.
Triangles ABD and CBD are congruent by the SAS Congruence Postulate.
Triangles ABD and CBD are similar by the SAS Similarity Postulate.

Answer 1

Let's go through each question one at a time.

Question 8:

For the similar triangles ΔAXY and ΔABC, if we want to find the length of segment AC, we can set up a proportion based on the similarity of the triangles. The expression that relates these segments can be formulated from the similarity:

Since AXY is similar to ABC, we can say that:

\[ \frac{AY}{AC} = \frac{AX}{AB} \]

We want to find an expression for AC. Rearranging the proportion, we get:

\[ AC = AB \cdot \frac{AY}{AX} \]

Thus, the correct answer is:
AC equals AB times AY over AX.

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Question 9:

We have a blimp that is 125 meters above the ground, with the camera hanging 10 meters below it. Therefore, the height of the camera from the ground is:

\[ 125 m - 10 m = 115 m \]

The blimp attachment is 20 meters long, which means that the effective height from point D down to point C is 20 meters corresponding to triangle EDF (where the height of 10 m is given).

Using similar triangles, the ground distance can be calculated as follows:

If triangle EDF has a height of 10 meters and the effective height when the camera is at 115 meters is 115 meters, we can set up a proportion:

Let AC be the ground distance:

\[ \frac{10 m}{20 m} = \frac{115 m}{AC} \]

Cross-multiplying gives us:

\[ 10 \cdot AC = 20 \cdot 115 \]

\[ AC = \frac{20 \cdot 115}{10} = 230 m \]

Please check if this calculation fits the format of the possible options provided, as none were derived directly from the provided answer choices. However, if options include relationships based on 250 or are based on factual segment lengths, 250 m could be used if corrections apply in practical contexts.

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Question 10:

In triangle ADC, segment DB is a median, and segment DB is also an angle bisector of ∠ADC.

Since DB is a median, it divides AC into two equal segments, which gives us:

\[ AB = BC \quad (i.e., \text{since } DB \text{ is a median}) \]

Since DB bisects the angle, we also know that:

\[ \frac{AB}{AC} = \frac{DB}{DC} \]

This scenario leads to the conclusion that triangles ABD and CBD are indeed congruent by the SAS (Side-Angle-Side) postulate (two sides and the included angle are equal). So, the best answer is:
Triangles ABD and CBD are congruent by the SAS Congruence Postulate.