Congruence Lesson 9-5

Congruence In chapter 6 we learned about similar figures. Similar figures have the same shape but not the same size. Congruent figures are exactly the same in shape and size. The symbol ~ means congruent. A X corresponding angles corresponding sides B C Z Y ABC ~ XYZ

Congruent Figures Congruent sides are noted by the slash marks on the X corresponding angles 15 45° 45° corresponding sides 45° B C Y 45° Z ABC ~ XYZ Congruent sides are noted by the slash marks on the Corresponding line segments.

Congruent Figures It’s easier to see the corresponding sides and angles when the figures are in matching positions. So sometimes you need to turn or flip one of the figures in order to find their corresponding sides or angles. corresponding angles A 45° 45° corresponding sides 45° B 45° C

Congruence Just as slash marks on the line segments indicate equal sides, arcs on the angles indicate equal angles.

Congruence There are three ways to identify whether triangles are congruent: If all three sides are equal (SSS) If all three sides are equal, then all the angles are Equal as well, therefore the triangles are congruent.

Congruence A second way is if 2 sides and the angle in between are equal then all sides and angles are equal and therefore congruent. Side-Angle-Side (SAS)

Congruence And the third way is if 2 angles and the side in between are the same, then the triangles are congruent. Angle-Side-Angle (ASA)

Try This Name the sides of the triangles that are congruent. A X B C Y Z

Try This Name the sides of the triangles that are congruent. AB and XY AC and XZ and BC and YZ A X B C Y Z

Try This Name the angles of the triangles that are congruent. A X B C Z

Try This Name the angles of the triangles that are congruent. X Angle A and X, Angle B and Y and Angle C and Z B C Y Z

Try This Give the reason that the following are congruent (example: SSS, SAS, ASA) 32 32 15 12 15 12

Try This Give the reason that the following are congruent (example: SSS, SAS, ASA) 32 32 SAS 15 12 15 12