Question 1

Question

Question 1
A)Which statement can verify the Triangle Inequality Theorem?(1 point)
Responses

An exterior angle is equal to its two remote interior angles.
An exterior angle is equal to its two remote interior angles.

The sum of any two sides of a triangle is greater than the length of the third side.
The sum of any two sides of a triangle is greater than the length of the third side.

The formula a2+b2=c2 will find the length of the third side of any triangle.
The formula  a squared plus b squared equals c squared  will find the length of the third side of any triangle.

The three angles of a triangle will always amount to 180 degrees.
The three angles of a triangle will always amount to 180 degrees.
Question 2
A)If a triangle has sides of 31 in. and 28 in., which is a possible length for the third side?(1 point)
Responses

59 in.
59 in.

3 in.
3 in.

62 in.
62 in.

33 in.
33 in.
Question 3
A)A ruler measuring 1 foot is bisected. Using your knowledge of constructions, determine the length of each segment of the bisected ruler.(1 point)
Responses

3 inches
3 inches

6 inches
6 inches

0.5 inch
0.5 inch

4 inches
4 inches
Question 4
A)
Use the image to answer the question.

On the left, two rays extend from a single point and a single arc passes through 2 points on the rays. On the right, an arc connects a point above a horizontal ray to a point on the ray.

What is the next step in this construction?

(1 point)
Responses

connecting point R to point S to create ∠SRQ
  connecting point  upper R to point  upper S to create  angle upper S upper R upper Q

creating a reference line with a straightedge
creating a reference line with a straightedge

connecting point Q to point S to create ∠SQR
connecting point  upper Q to point  upper S to create  angle upper S upper Q upper R

placing the compass point on the vertex and drawing an arc
placing the compass point on the vertex and drawing an arc
Question 5
A)If an angle can be divided in half by constructing a bisector, then what method doubles an angle?(1 point)
Responses

constructing a copy attached to the original angle
constructing a copy attached to the original angle

bisecting the angle twice
bisecting the angle twice

constructing two of the bisected angles
constructing two of the bisected angles

constructing a copy of the bisected angle attached to the original angle

GPT-4o mini · Answer

Here are the responses for each of the questions based on your descriptions:

Question 1: A) Which statement can verify the Triangle Inequality Theorem?
Response: The sum of any two sides of a triangle is greater than the length of the third side.

Question 2: A) If a triangle has sides of 31 in. and 28 in., which is a possible length for the third side?
Response: 33 in.
(This satisfies the Triangle Inequality Theorem: 31 + 28 > 33, 31 + 33 > 28, and 28 + 33 > 31.)

Question 3: A) A ruler measuring 1 foot is bisected. Using your knowledge of constructions, determine the length of each segment of the bisected ruler.
Response: 6 inches
(A foot is equal to 12 inches, so half of that is 6 inches.)

Question 4: A) Use the image to answer the question.
What is the next step in this construction?
Response: placing the compass point on the vertex and drawing an arc
(This step typically follows when creating angle constructions using a compass and straightedge.)

Question 5: A) If an angle can be divided in half by constructing a bisector, then what method doubles an angle?
Response: constructing a copy of the bisected angle attached to the original angle
(This method creates an angle that is twice the size of the original angle.)

You can review these answers and make any adjustments if needed!