Question

1. what does the aa criterion stand for in triangle similarity?

a. angle-angle
b. altitude-angle
c. angle-axis
d. axis-angle

1. in triangle δabc, ab = 9 cm, bc = 12 cm, and ac = 15 cm. in triangle δdef, de = 18 cm, ef = 24 cm. what is the length of df if the triangles are similar?

a. 40 cm
b. 35 cm
c. 30 cm
d. 20 cm

1. if a building is 100 meters tall and you want to create a scale drawing using a scale factor of 0.1, what will be the height of the building in the scale drawing?

a. 8 meters
b. 12 meters
c. 10 meters
d. 5 meters

Explanation:

Question 1

The AA (Angle - Angle) criterion for triangle similarity states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. The other options (Altitude - Angle, Angle - Axis, Axis - Angle) are not related to the standard triangle similarity criterion.

Step 1: Find the scale factor

First, we find the scale factor between the two similar triangles. We can use the corresponding sides \(AB\) and \(DE\). The length of \(AB = 9\space cm\) and \(DE=18\space cm\). The scale factor \(k=\frac{DE}{AB}=\frac{18}{9} = 2\).

Step 2: Find the length of \(DF\)

Since the triangles are similar, the ratio of corresponding sides is equal. The side \(AC\) in \(\triangle ABC\) corresponds to side \(DF\) in \(\triangle DEF\). We know that \(AC = 15\space cm\). So, \(DF=k\times AC\). Substituting the value of \(k = 2\) and \(AC = 15\space cm\), we get \(DF=2\times15=30\space cm\).

Step 1: Recall the scale factor formula

The height of the object in the scale drawing \(h_{drawing}\) is given by the formula \(h_{drawing}=h_{actual}\times\text{scale factor}\).

Step 2: Substitute the values

We know that \(h_{actual}=100\space meters\) and the scale factor \(= 0.1\). So, \(h_{drawing}=100\times0.1 = 10\space meters\).

Answer:

a. Angle - Angle

Question 2