We compared all our triangles to confirm that they were indeed congruent. Apart from human error, we proved it to be true.
Then we constructed triangles with 2 given angles and a given side length between them (angle, side, angle or A.S.A).
Once we completed our A.S.A triangle. We measured the third angle and the other two sides and compared our findings. All triangles were CONGRUENT!
We continued our investigation of triangles and congruence. I gave students three angle measurements (A.A.A). The all constructed a triangle with the given measurements. We began by drawing a base line. Then using our protractor, we measured one of the given angles at one end of the line. We drew a long line segment to create the angle. Afterwards, we measured a second given angle at the other end of the line, drawing another long line segment. Where the line segments crossed, the third angle was constructed on its own. Even if we had only been given two angle measurements, we would have been able to determine the third angle without measuring because we know the sum of the interior angles of a triangle is 180 degrees. Click on the below link for a quick view.
How to Construct a Triangle When Given the Angles
After constructing these triangles, we determined that since our side lengths were different, our triangles could not be congruent. We postulated that our triangles would all be similar, but we ran out of time to investigate this theory.
Tomorrow we will begin by proving or disproving this statement: When given three angle measurements, triangles are SIMILAR. TRUE OR FALSE?
MATH VOCABULARY: CONGRUENT VS SIMILAR
congruent
• having the same shape and the same size.
EXAMPLES:
similar
• having the same shape but not necessarily the same size.
EXAMPLES:
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