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 ©curriculum associates, llc copying is 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
Since two angles of $\triangle XYW$ are equal to two angles of $\triangle XWZ$ (Angle - Angle similarity), $\triangle XYW\sim\triangle XWZ$.
# Answer:
Yes, $\triangle XYW\sim\triangle XWZ$ by the AA - similarity criterion.

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

### 3c.
# Explanation:
## Step1: Check for equal angles
In $\triangle XYW$ and $\triangle WYZ$, $\angle XYW=\angle WYZ = 90^{\circ}$. But we don't have information about other angle equalities.
## Step2: Conclude similarity
Since we cannot show that two pairs of angles are equal, $\triangle XYW$ and $\triangle WYZ$ are not necessarily similar.
# Answer:
No, there is not enough information to show that $\triangle XYW\sim\triangle WYZ$.

### 4a.
# Explanation:
## Step1: Identify equal angles
Given $\angle C\cong\angle F$, and $\angle BDC=\angle FDE$ (vertical angles are equal).
## Step2: Apply AA - similarity
By the AA - similarity criterion, $\triangle BCD\sim\triangle EFD$.
# Answer:
$\triangle EFD$ is similar to $\triangle BCD$.

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

### 5 (assuming the figure shows two right - angled triangles with sides in proportion)
# Explanation:
## Step1: Check for similarity
If the two triangles are right - angled and the ratios of their corresponding sides are equal. Let the two right - angled triangles have sides such that $\frac{x}{9}=\frac{20}{y}$ (assuming appropriate side - pairings). If the triangles are similar by the Side - Angle - Side (SAS) similarity (if the included angles are right angles) or by the Hypotenuse - Leg (HL) similarity (if they are right - angled and the ratios of hypotenuse and one leg are equal).
Let's assume the triangles are similar by the ratio of sides. If we assume the triangles are similar and the ratio of corresponding sides gives $\frac{x}{9}=\frac{20}{15}$ (assuming the other side of the second triangle is 15 based on similar - triangle side - length relationships).
## Step2: Solve for $x$
Cross - multiply: $15x=20\times9$, so $15x = 180$, then $x=\frac{180}{15}=12$.
# Answer:
Yes, the triangles are similar (assuming appropriate side - length and angle relationships). $x = 12$.

Since the figure for 6 is not fully described, we cannot answer 6 completely. But the general approach would be to check for angle equalities (AA - similarity), side - length ratios (SSS - similarity), or a combination of side and angle relationships (SAS - similarity) to determine similarity and then solve for $x$ if applicable.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

3a.

Step1: Identify equal angles

Step2: Apply AA - similarity criterion

Step1: Analyze angle measures

Step2: Determine similarity

Step1: Check for equal angles

Step2: Conclude similarity

Answer:

3b.