Question 1041083: This figure shows a quadrilateral made of triangle ABF and triangle DEC.
https://byuis.brainhoney.com/Resource/46824920,0/Assets/Media/Images/41.4.HOT2.quad.jpg
a. What does it mean for triangles to be congruent?
b. Jane is told that angle A is congruent to angle D and angle B is congruent to angle E. She concludes that the triangles are congruent because of AAA. Explain why she thinks this, and whether or not you think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane and George have been given? Explain why you think this.
Thanks in advance!
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Labeling is different than expected but call the upper case letters as points.
Points B and C name the same point.
Points F and E name the same point.
(a) the two triangles have the same angle measures and the same length measures for their corresponding parts. Their orientations are different but their corresponding parts are of equal measures.
(b) AAA says nothing about the sides of the triangles, but the two triangles share one corresponding side, so this should be enough to say that the two triangles are congruent, ... ASA Theorem (two angles and the included side between them.)
(c) Good for George! See what is discussed in (b).
|
|
|
