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IM Geo.2.7 Practice: Angle-Side-Angle Triangle Congruence

What triangle congruence theorem could you use to prove triangle  is congruent to triangle ?

Han wrote a proof that triangle BCD is congruent to triangle DAB.

Han's proof is incomplete.

  • Line  is parallel to line  and cut by transversal . So angles  and  are alternate interior angles and must be congruent.
  • Side  is congruent to side  because they're the same segment.
  • Angle  is congruent to angle because they're both right angles.
  • By the Angle-Side-Angle Triangle Congruence Theorem, triangle  is congruent to triangle 
How can Han fix his proof?

Segment GE is an angle bisector of both angle HEF and angle FGH.

Prove triangle is congruent to triangle .

Triangles ACD and BCD are isosceles.

Angle  has a measure of 33 degrees and angle  has a measure of 35 degrees. Find the measure of angle .

Which conjecture is possible to prove?

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  • B
  • C
  • D
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Andre is drawing a triangle that is congruent to this one.

He begins by constructing an angle congruent to angle What is the least amount of additional information that Andre needs to construct a triangle congruent to this one?

Here is a diagram of a straightedge and compass construction.

 is the center of one circle, and B is the center of the other.  Which segment has the same length as segment ?

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  • A
  • B
  • C
  • D
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