Answers 2026 FPC SAP 1206315-Geometry CR S2Triangle Similarity: SSS and SAS (Sec 7-3, 7-4, 7-5)

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Which best explains whether or not all isosceles triangles are similar?

All isosceles triangles are similar. Two angles within each triangle are always congruent.

All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined.

All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

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Triangle A B C is cut by line segment M N. Line segment M N goes from side A B to side B C and cuts both sides into equal parts. The lengths of A M and M B are 88 centimeters, the lengths of C N and N B are 75 centimeters, and the length of A C is 116 centimeters.

58 cm

75 cm

88 cm

116 cm

Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not?

Yes, they both partition the segment into a 1:3 ratio.

Yes, they are both the distance from one endpoint to the other.

No, P is the distance from A to B, and Q is the distance from B to A.

No, Q is closer to A and P is closer to B.

Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C.

a reflection and a dilation

a rotation and a dilation

a translation and a dilation

a reflection and a translation

Two similar triangles are shown.

translated

reflected

dilated

rotated

Point O is the center of dilation. Triangle D E F is dilated to create smaller triangle D prime E prime F prime. The length of O F prime is 3. The length of F prime F is 7.