lesson 7 | session 3
3 a. is △xyw ~ △xwz? explain why or why not.
b. is △wyz ~ △xwz? explain why or why not.
c. is △xyw ~ △wyz? explain why or why not.
4 in the figure at the right, ∠c≅∠f.
a. which triangle is similar to △bcd?
b. which triangle is similar to △ace?
5 can you use the information in the figure to show that the triangles are similar? explain. if so, find the value of x.
6 can you use the information in the figure to show that the triangles are similar? explain. if so, find the value of x.
154 lesson 7 describe angle relationships in triangles
downloaded by r. brown. this resource expires on 6/30/2024.

Question

Accepted Answer

### 3a.
# Explanation:
## Step1: Identify equal angles
In $\triangle XYW$ and $\triangle XWZ$, $\angle XYW=\angle XWZ = 90^{\circ}$, and $\angle X$ is common to both triangles.
## Step2: Apply AA - similarity criterion
By the Angle - Angle (AA) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), $\triangle XYW\sim\triangle XWZ$.
# Answer:
Yes, $\triangle XYW\sim\triangle XWZ$ because $\angle XYW=\angle XWZ = 90^{\circ}$ and $\angle X$ is common.

### 3b.
# Explanation:
## Step1: Analyze angle - angle relationship
In $\triangle WYZ$ and $\triangle XWZ$,  $\angle WYZ = 90^{\circ}$ and $\angle XWZ=90^{\circ}$, but we do not have information about another pair of equal non - right angles.
## Step2: Determine similarity
Since we cannot show that two pairs of angles are equal, $\triangle WYZ$ is not necessarily similar to $\triangle XWZ$.
# Answer:
No, we cannot show that two pairs of angles are equal.

### 3c.
# Explanation:
## Step1: Analyze angle - angle relationship
In $\triangle XYW$ and $\triangle WYZ$, $\angle XYW=\angle WYZ = 90^{\circ}$, but we do not have information about another pair of equal non - right angles.
## Step2: Determine similarity
Since we cannot show that two pairs of angles are equal, $\triangle XYW$ is not necessarily similar to $\triangle WYZ$.
# Answer:
No, we cannot show that two pairs of angles are equal.

### 4a.
# Explanation:
## Step1: Identify equal angles
Since $\angle C=\angle F$ and $\angle BDC=\angle EDF$ (vertically opposite angles), by the AA - similarity criterion.
## Step2: Determine similar triangle
$\triangle BCD\sim\triangle EFD$.
# Answer:
$\triangle EFD$

### 4b.
# Explanation:
## Step1: Identify equal angles
Since $\angle C=\angle F$ and $\angle A$ is common to $\triangle ACE$ and $\triangle AFD$.
## Step2: Determine similar triangle
By the AA - similarity criterion, $\triangle ACE\sim\triangle AFD$.
# Answer:
$\triangle AFD$

### 5.
# Explanation:
## Step1: Check for equal angles
The two triangles have right angles. Also, the vertical angles are equal. So, by the AA - similarity criterion, the triangles are similar.
## Step2: Set up proportion
If the triangles are similar, then the ratios of corresponding sides are equal. We have $\frac{x}{9}=\frac{20}{15}$.
## Step3: Solve for x
Cross - multiply: $15x=20\times9$, so $15x = 180$, and $x=\frac{180}{15}=12$.
# Answer:
Yes, the triangles are similar by AA - similarity. $x = 12$

### 6.
# Explanation:
## Step1: Check for equal angles
The two triangles have equal angles (by the AA - similarity criterion, since the angles formed by the parallel sides are equal).
## Step2: Set up proportion
The ratios of corresponding sides are equal. $\frac{4}{x}=\frac{5}{7}$.
## Step3: Solve for x
Cross - multiply: $5x=4\times7$, so $5x = 28$, and $x=\frac{28}{5}=5.6$.
# Answer:
Yes, the triangles are similar. $x = 5.6$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

3a.

Step1: Identify equal angles

Step2: Apply AA - similarity criterion

Step1: Analyze angle - angle relationship

Step2: Determine similarity

Step1: Analyze angle - angle relationship

Step2: Determine similarity

Answer:

3b.