Congruent and Similar Triangles

  1. and intersect at O.
is perpendicular to and is perpendicular to .
Which geometric statement could be used to prove that triangle ACO is congruent to triangle BDO?
A) SSSB) SAS C) AA D) ASA /
  1. Given the triangle ABC below:

Which of the following triangles is congruent to triangle ABC?

A) / / C) /
B) / / D) /
  1. Consider triangle RST shown here on the right.

Which of the following triangles is definitely congruent to triangle RST?

A)C)

B) D)

  1. In the following four figures, point E is the intersection of lines PQ and RS.

Which of these figures are triangles PES and QER necessarily similar?

A)C)

B) D)

  1. Four pairs of triangles are illustrated below.

1) / / 3) /
2) / / 4) /

Which pairs of triangles are necessarily similar?

A) / 1 and 3 / C) / 2 and 3
B) / 1 and 4 / D) / 2 and 4
  1. Triangle RST is shown on the right

Which of the triangles below is not necessarily similar to triangle RST?

A) / / C) /
B) / / D) /
  1. Consider triangle LMN shown below.

Which of the following triangles is definitely congruent to triangle LMN?

  1. In parallelogram ABCD, diagonals AC and BD intersect at point O.
Statement / Justification
1. / 1.The opposites sides of a parallelogram are congruent.
2. / 2.The diagonals of a parallelogram bisect each other.
3. / 3.The diagonals of a parallelogram bisect each other.
4.AOB COD / 4.

Which of the statements below is the reason for step 4?

A) / Two triangles are congruent if two sides and the contained angle of one triangle are congruent to two sides and the contained angle of the other triangle. (SAS)
B) / Two triangles are congruent if the three pairs of corresponding sides are congruent. (SSS)
C) / Two triangles are congruent if two angles and the contained side of one triangle are congruent to two angles and the contained side of the other triangle. (ASA)
D) / Two triangles are congruent if two pairs of corresponding angles are congruent. (AA)
  1. In triangles ABY and AXC shown below, and .

Which one of the following statements could be used to prove that triangle ABY is congruent to triangle ACX?

A) / If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.(SSS)
B) / If two sides and a contained angle of one triangle are congruent to two sides and the contained angle of another triangle, then the triangles are congruent.(SAS)
C) / If two angles and a contained side of one triangle are congruent to two angles and the contained side of another triangle, then the triangles are congruent.(ASA)
D) / If two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.(AA)
  1. Each diagram compares two figures. Which statement is NOT necessarily true?

A) /
Square ACDE is similar to square ABGF. / C) /
Rectangle ACDE is similar to rectangle ABGF.
B) /
Triangle ABC is similar to triangle EDC. / D) /
Triangle ABC is similar to triangle DEC.
  1. Which of the following pairs of figures is necessarily a similarity transformation?

A) / / C) /
B) / / D) /
  1. Given ∆ABC below, choose the triangle that would be congruent to ∆ABC.
  1. In the following diagram, is an angle bisector os and . Using a statement and justification table, prove that m.
  1. In the diagram is the perpendicular bisector of side . Using a statement an justification table, prove that ∆BDA∆CDA.