Unit 2, Lesson 7

Angle-Side-Angle Triangle Congruence

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Integrated Math 1

Practice

Problem 1

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

<p>Triangle ADE and CBE where angle DAE is congruent to and BCE. CE is congruent to AE.</p>

Practice

Problem 2

Han wrote a proof that triangle is congruent to triangle . Han's proof is incomplete. How can Han fix his proof?

<p>Line DC is parallel to and above line AB and cut by transversal DB. Angles A and C are right angles.</p>

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 .

Problem 3

Segment is an angle bisector of both angle and angle . Prove triangle is congruent to triangle .

<p>Quadrilateral E F G H. Segment G E is drawn in, dividing the shape into 2 triangles.</p>

Problem 4

ForLesson 6: Side-Angle-Side Triangle Congruence

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

<p>Triangle ACD with point B near the center. Segments BD, BC, and BA are drawn. Line segment BD is congruent to BC.</p>

Problem 5

ForLesson 5: Points, Segments, and Zigzags

Which conjecture is possible to prove?

All triangles with at least one side length of 5 are congruent.
All pentagons with at least one side length of 5 are congruent.
All rectangles with at least one side length of 5 are congruent.
All squares with at least one side length of 5 are congruent.

Problem 6

ForLesson 4: Congruent Triangles, Part 2

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?

Problem 7

ForLesson 1: Build It

Here is a diagram of a straightedge and compass construction. is the center of one circle, and is the center of the other. Which segment has the same length as segment ?

<p>Two circles, one large centered at point C. Points A, B, and D lie on the large circle. The smaller circle centered at point B intersects larger circle at points A and D. Radii CA, CB, and CD are drawn. Radii BA and BD are drawn.</p>

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Angle-Side-Angle Triangle Congruence

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7