• angle — is included between sides ab and ac.
• angle — is included between sides ab and bc.
• angle — is included between sides ac and bc.

5) practice: using visual cues and summarizing
list all the possible ways to name the triangle at right.

6) practice: activating prior knowledge and organizing information
write the correct number in each blank to complete the review list.
review: triangle facts
• they are closed — dimensional figures.
• they are formed by — segments that connect — noncollinear points.
• they have exactly — sides, — angles, and — vertices.
• each side is included between — angles and is opposite — angle.
• each angle is included between — sides and is opposite — side.

7) practice: using visual cues
give one reason why each figure below is not a triangle.

Question

• angle — is included between sides ab and ac.
• angle — is included between sides ab and bc.
• angle — is included between sides ac and bc.

5) practice: using visual cues and summarizing
list all the possible ways to name the triangle at right.

6) practice: activating prior knowledge and organizing information
write the correct number in each blank to complete the review list.
review: triangle facts
• they are closed — dimensional figures.
• they are formed by — segments that connect — noncollinear points.
• they have exactly — sides, — angles, and — vertices.
• each side is included between — angles and is opposite — angle.
• each angle is included between — sides and is opposite — side.

7) practice: using visual cues
give one reason why each figure below is not a triangle.

Accepted Answer

# Explanation:
## Step1: Recall Triangle Basics
Triangles are 2 - dimensional closed figures. They are formed by 3 line segments connecting 3 non - collinear points. A triangle has 3 sides, 3 angles, and 3 vertices. Each side is included between 2 angles and is opposite 1 angle. Each angle is included between 2 sides and is opposite 1 side.
## Step2: Fill in the Blanks
- "They are closed $\boldsymbol{2}$ - dimensional figures." (Since triangles are planar, 2 - D)
- "They are formed by $\boldsymbol{3}$ segments that connect $\boldsymbol{3}$ noncollinear points." (By definition of a triangle)
- "They have exactly $\boldsymbol{3}$ sides, $\boldsymbol{3}$ angles, and $\boldsymbol{3}$ vertices." (Basic properties of a triangle)
- "Each side is included between $\boldsymbol{2}$ angles and is opposite $\boldsymbol{1}$ angle." (For example, in $\triangle ABC$, side $BC$ is between $\angle B$ and $\angle C$, and opposite $\angle A$)
- "Each angle is included between $\boldsymbol{2}$ sides and is opposite $\boldsymbol{1}$ side." (In $\triangle ABC$, $\angle A$ is between $AB$ and $AC$, and opposite $BC$)

For the angle inclusion questions (first three bullet points, assuming the triangle is $\triangle ABC$):
- Angle $\angle A$ is included between sides $AB$ and $AC$.
- Angle $\angle B$ is included between sides $AB$ and $BC$.
- Angle $\angle C$ is included between sides $AC$ and $BC$.

For naming the triangle (question 5, triangle $DEF$ with right angle at $F$):
Possible names: $\triangle DEF$, $\triangle DFE$, $\triangle EDF$, $\triangle EFD$, $\triangle FDE$, $\triangle FED$, and also by its type (right - angled triangle at $F$, so right triangle $DEF$ or right triangle $DFE$ etc.)

For question 7 (figures not shown, but common reasons a figure is not a triangle: not closed, less than 3 sides, sides not straight, points collinear etc.)

# Answer:
### For the "REVIEW: Triangle Facts" blanks:
- They are closed $\boldsymbol{2}$ - dimensional figures.
- They are formed by $\boldsymbol{3}$ segments that connect $\boldsymbol{3}$ noncollinear points.
- They have exactly $\boldsymbol{3}$ sides, $\boldsymbol{3}$ angles, and $\boldsymbol{3}$ vertices.
- Each side is included between $\boldsymbol{2}$ angles and is opposite $\boldsymbol{1}$ angle.
- Each angle is included between $\boldsymbol{2}$ sides and is opposite $\boldsymbol{1}$ side.

### For the angle inclusion (assuming triangle $ABC$):
- Angle $\boldsymbol{\angle A}$ is included between sides $AB$ and $AC$.
- Angle $\boldsymbol{\angle B}$ is included between sides $AB$ and $BC$.
- Angle $\boldsymbol{\angle C}$ is included between sides $AC$ and $BC$.

### For naming triangle $DEF$ (right - angled at $F$):
Possible names: $\triangle DEF$, $\triangle DFE$, $\triangle EDF$, $\triangle EFD$, $\triangle FDE$, $\triangle FED$, Right - angled triangle $DEF$ (at $F$), etc.

### For question 7 (example reason for a non - triangle figure, e.g., if a figure has 4 sides, reason: "The figure has more than 3 sides" or "The points are collinear" or "The figure is not closed")

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall Triangle Basics

Step2: Fill in the Blanks

Answer:

For the "REVIEW: Triangle Facts" blanks:

For the angle inclusion (assuming triangle \(ABC\)):

For naming triangle \(DEF\) (right - angled at \(F\)):

For question 7 (example reason for a non - triangle figure, e.g., if a figure has 4 sides, reason: "The figure has more than 3 sides" or "The points are collinear" or "The figure is not closed")