Question

1. what does the sas criterion state for triangle congruence?

a. three sides of one triangle are equal to three sides of another triangle
b. two sides and the included angle
c. two sides and a non - included angle
d. two angles and a non - included side

1. triangle xyz has sides ( xy = 3 ), ( yz = 5 ), and ( xz = 6 ). which set of side lengths ensures triangle abc is congruent to triangle xyz by sss?

a. ( ab = 6 ), ( bc = 8 ), ( ac = 4 )
b. ( ab = 3 ), ( bc = 6 ), ( ac = 5 )
c. ( ab = 3 ), ( bc = 5 ), ( ac = 6 )
d. ( ab = 6 ), ( bc = 3 ), ( ac = 5 )

1. which tool is essential for constructing a triangle using the asa method in geogebra?

a. intersect two objects
b. distance or length
c. angle with given size
d. compass

1. which is an example of an included angle in a triangle?

a. the angle between the two given sides
b. any angle that measures 90 degrees
c. the largest angle in the triangle
d. the angle opposite one of the given sides

1. which of the following is necessary for two triangles to be congruent by asa?

a. one pair of congruent sides and any angle
b. two pairs of congruent angles and the included side
c. three pairs of congruent sides
d. two pairs of congruent sides

1. which of the following correctly represents the asa criterion?

a. three sides
b. one side and two angles
c. two angles and the included side
d. two angles and one adjacent side

1. which triangle property is used to determine when a triangle can be uniquely constructed given three sides?

a. angle - side - angle
b. side - angle - side
c. side - side - side
d. angle - angle - side

Explanation:

• Question 15: The SAS (Side - Angle - Side) criterion states that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• Question 16: For SSS (Side - Side - Side) congruence, the sides of triangle \(ABC\) must match the sides of triangle \(XYZ\). Given \(XY = 3\), \(YZ=5\), \(XZ = 6\), we need \(AB = 3\), \(BC = 5\), \(AC = 6\).
• Question 17: When constructing a triangle using the ASA (Angle - Side - Angle) method in GeoGebra, the "Angle with Given Size" tool is essential to construct the angles.
• Question 18: An included angle in a triangle is the angle between the two given sides.
• Question 19: For two triangles to be congruent by ASA, two pairs of congruent angles and the included side are required.
• Question 20: The ASA criterion is represented by two angles and the included side.
• Question 21: The SSS (Side - Side - Side) property is used to determine if a triangle can be uniquely constructed given three sides.

Answer:

1. B. Two sides and the included angle
2. C. \(AB = 3\), \(BC = 5\), \(AC = 6\)
3. C. Angle with Given Size
4. A. The angle between the two given sides
5. B. Two pairs of congruent angles and the included side
6. C. Two angles and the included side
7. C. Side - Side - Side