13.4/13.5/13.6 – SAS, ASA, AAS Congruency Theorems
Name _____________________________________________________
1.
A. Use the distance formula and a protractor to prove that the two triangles shown on the grid are congruent by SAS.
Show your work.
B. Mark the triangles to show which sides and angles are congruent.
C. Write a congruency statement for the triangles.
2. Emerson wants to translate
and then reflect it over the y-axis to form a new triangle in Quadrant II. She uses
what she knows about transformations to determine the vertices of
before performing the transformations.
A. Briefly describe how Emerson can use the ASA Congruence Theorem to
determine whether or not
she transformed
such that the image is congruent to the pre-image.
B. Connect points A’, B’, and C’. Determine the measure of two
corresponding angles in each triangle. Label the angle measures on the
triangles.
C. Determine the length of the included side of
and
. Show your work.
3. Describe and use AAS to prove that triangle LMN is congruent to triangle QRS.
4. Triangles ABC and DFG are given.
A. Side ̅̅̅̅ of
is congruent to ̅̅̅̅ of
. Mark the triangles to show that these sides are congruent.
B. Do you have enough information to determine whether
congruent to
? Explain your reasoning.
C. Without using a protractor, calculate the measure of
is
. Show your work. Write the measure on the triangle.
D. Now do you have enough information to determine whether
is congruent to
statements for corresponding sides and angles to justify your reasoning.
5. Determine whether
SAS.
is congruent to
by
6. Determine whether
ASA.
? Write congruence
is congruent to
by
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