Download (2) The shape made by the student is not a triangle because the

(2) The shape made by the student is not a triangle because the bottom side does
not match up with the other sides. I would give the student no points for this
problem.
Since the triangles are congruent DE = AB = 22.1 cm
Since the triangles are congruent DF = AC = 14.1 cm
Since the triangles are congruent BC = EF = 26.1 cm
Since the triangles are congruent the measure of angle A is the same as
the measure of angle D, so angle A measures 89 degrees.
(e) Since the triangles are congruent the measure of angle B is the same as
the measure of angle E, so angle B measures 33 degrees.
(f) Since the triangles are congruent the measure of angle F is the same as
the measure of angle C, so angle F measures 58 degrees.
(7) (a)
(b)
(c)
(d)
(11) (a) Both triangles have sides of lengths 30, 40, and 20 ft. By the S-S-S
postulate, the triangles are congruent.
(b) Both triangles have sides of lengths 26 and 22 km with an angle of 33
degees between them. Hence they are congruent by the S-A-S postulate.
(c) The first triangle has angles of 46 and 77 degrees. So the third angle has
measure 180 − 46 − 77 = 57 degrees. The second triangle has angles of 46
and 78 degrees, so its third angle has measure 180 − 46 − 78 = 56 degrees.
Hence the triangles have angles of different degrees and so they are not
congruent.
(15) (a) We know that BC = DC and AC = AC. Also angle ACB and angle
ACD are both right angles. Hence by the S-A-S postulate, the two
triangles are congruent.
(b) We know that F G = GH. Also angle F is congruent to angle H and
angle EGF is congruent to angle IGH. Hence by the A-S-A postulate,
the two triangles are congruent.
(17) (a) The two triangles have 2 pairs of congruent angles, and the sides of each
triangle between the congruent angles are congruent. Hence by the A-S-A
postulate, the triangles are congruent.
(b) Since the triangles are congruent, the side between the tent and the tree
is congruent to the side across the canyon. So if you measure the distance
from the tent to the tree, you can find the distance across the canyon.
(20) (a) We know that angle B is congruent to angle D and that angle ACB is
congruent to angle ECD. So if BC is congruent to CD then we can use
the A-S-A postulate to conclude that the triangles are congruent.
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(b) We know that angle G is congruent to angle L and that F G is congruent
to LK. So if we know that angle F is congruent to angle K then we can
use the A-S-A postulate to conclude that the triangles are congruent.
Alternatively, if we know instead that GH is congruent to JL, then we
can conclude that the triangles are congruent by the S-A-S postulate.
(24) The student chose the wrong sides to be congruent. Corresponding sides of
congruent triangles are congruent, so AB is congruent to XY and Y Z is
congruent to BC but we can’t conclude that AB is congruent to Y Z. I would
encourage the student to review the definition and properties of congruent
triangles.
(25) An activity I would do is to pass out ruler, pens and papers to all the students.
I would first have the students draw a line that is 5 inches long, then I would
have them draw another line from the same endpoint that is 4 inches long.
Finally I would have them connect their lines to make a triangle. Now each
of the students’ triangles have two congruent sides; however, the third side is
going to have a different length based on the angle that each student made,
and so their triangles will not all be congruent. This shows that it’s not enough
to have 2 congruent sides for the triangle to be congruent.