Which of the following statements is incorrect?
a) a triangle with three congruent sides is equilateral
b) the Isosceles Triangle Theorem can be used with equilateral triangles
c) SAS, AAS, SSA, and SSS are correct congruency shortcuts
d) a triangle with three congruent sides is isosceles
c) SAS, AAS, SSA< and SSS are correct congruency shortcuts
SSA is not a correct congruency shortcut
Triangle 1 is transformed to create Triangle 2 such that sides AB and BC are congruent to sides XY and YZ respectively. Angle B is congruent to angle Y. Fill in the blank with the correct shortcut and angle.
Triangle ABC must be congruent to triangle XYZ because of the _____ theorem. Thus, angle BAC must be congruent to angle _____.
1) SAS
2) YXZ
In triangles ABC and DEF, AB=FD and angle A=angle D. What will make the two triangles congruent by SAS?
a) angle B=angle c
b) AC=FD
c) AC=DE
d) AB=DE
c) AC=DE
Which of the following is a valid Triangle Congruence Theorem?
a) AAA
b) ASA
c) SSA
d) None of the above
b) ASA
Two geometrical figures are said to be congruent if they are ___ in every respect.
a) adjacent
b) dissimilar
c) identical
d) different
c) identical
If two corresponding angles and a non-including side of two triangles are equal, then the triangles are congruent by ___ criterion.
AAS
Which of the following measurements of sides and angles are required to prove congruence using the AAS theorem?
a) two sides and the non-included angle
b) two angles and the non-included side
c) two sides and the included angle
d) two angles and the included side
b) two angles and the non-included side
Which of the following is the symbol of congruence?
a)
b)
c)
d) ≅
d) ≅
If two triangles share a corresponding side and have congruent angles on both ends of that side, what is the congruency statement for the triangles?
The triangles are congruent by ASA
Two triangles XYZ and STU are said to be congruent by ASA criteria. Which of the following is correct?
a) angle X=angle S
b) angle Z=angle U
c) XZ=SU
d) all of the above
d) all of the above
What kind of triangle does HL apply to?
A right triangle
In SAS theorem, the angle A refers to...
a) any interior angle
b) angle
c) the included angle
d) the non-included angle
c) the included angle
Name the theorem that would best prove triangle congruence based on the following description. Two triangles have two pairs of congruent angles and one pair of congruent sides.
AAS
Right triangle ABC and right triangle XYZ are congruent. If angle A=31 and angle Z=59, what is angle C?
Angle C=59
If three sides of a triangle are equal to three sides of another triangle, then the two triangles are congruent. This is ___ condition for congruence.
SSS