Question

directions: determine whether the triangles are similar by aa-, sss-, sas-, or not similar. if the triangles are similar, write a valid similarity statement. this is a 2 - page document! per: unit 6: similar triangles homework 3: proving triangles are similar 1. 2. 3. 4. 5. 6. 7. 8.

Explanation:

Step1: Recall similarity criteria

We have AA (angle - angle), SSS (side - side - side) and SAS (side - angle - side) criteria for triangle similarity.

Step2: For the first - pair of triangles $\triangle RST$ and $\triangle QNP$

Calculate the ratios of corresponding sides. $\frac{RS}{QN}=\frac{44}{17}$, $\frac{ST}{NP}=\frac{55}{20}=\frac{11}{4}$, $\frac{RT}{QP}=\frac{37.4}{25}$. Since $\frac{44}{17}
eq\frac{11}{4}
eq\frac{37.4}{25}$, the triangles are not similar by SSS.

Step3: For other pairs

We need to check angles and side - length ratios. For example, if we have two pairs of equal angles, we can use AA criterion. If the ratios of all three pairs of corresponding sides are equal, we use SSS criterion. If two pairs of sides are in proportion and the included angles are equal, we use SAS criterion.
Let's take another example: For a pair of triangles where we know two angles of one triangle are equal to two angles of another triangle, say $\angle A=\angle D$ and $\angle B=\angle E$ in $\triangle ABC$ and $\triangle DEF$, then $\triangle ABC\sim\triangle DEF$ by AA criterion.

1. $\triangle RST$ and $\triangle QNP$: Not similar.
2. (No data for angles and sides given for this pair in the step - by - step so far, but follow the same process of checking AA, SSS, SAS).
3. (Check side - length ratios and angles).
4. In $\triangle ANF$ and $\triangle HES$, we have $\angle A = 29^{\circ}$, $\angle N=106^{\circ}$, $\angle H = 45^{\circ}$, $\angle S = 29^{\circ}$. Since only one pair of angles is equal, they are not similar by AA.
5. (Check side - length ratios).
6. For $\triangle CED$ and $\triangle LMN$: $\frac{CE}{LM}=\frac{96}{54}=\frac{16}{9}$, $\frac{CD}{LN}=\frac{64}{45}$, $\frac{ED}{MN}=\frac{80}{36}=\frac{20}{9}$. Since the ratios are not equal, they are not similar by SSS.
7. (Check for parallel lines or angle - equalities to use AA, SSS, SAS).
8. (Check side - length ratios and angles).

Answer:

1. Not similar
2. (Answer depends on further analysis of angles and sides)
3. (Answer depends on further analysis of angles and sides)
4. Not similar
5. (Answer depends on further analysis of angles and sides)
6. Not similar
7. (Answer depends on further analysis of angles and sides)
8. (Answer depends on further analysis of angles and sides)