WEBVTT
1
00:00:00.240 --> 00:00:02.669 A:middle L:90%
to solve this problem. We will be using the
2
00:00:02.669 --> 00:00:06.320 A:middle L:90%
converse of the hinge there. Um, which states
3
00:00:06.349 --> 00:00:10.820 A:middle L:90%
, if you have your corresponding and congruent sides.
4
00:00:10.820 --> 00:00:13.710 A:middle L:90%
So we've got this side on the left on the
5
00:00:13.710 --> 00:00:17.230 A:middle L:90%
side on the right are marked congruent. We also
6
00:00:17.230 --> 00:00:20.350 A:middle L:90%
know that we've got a shared side that is congratulated
7
00:00:21.640 --> 00:00:26.940 A:middle L:90%
. But we also know the included angle between our
8
00:00:27.109 --> 00:00:33.530 A:middle L:90%
corresponding congruent sides and because of the sides opposite of
9
00:00:33.530 --> 00:00:37.780 A:middle L:90%
are included, angles are not congruent the converse of
10
00:00:37.780 --> 00:00:41.850 A:middle L:90%
Hinge. Therm says the angles are not congruent.
11
00:00:42.469 --> 00:00:46.530 A:middle L:90%
The angle opposite of the largest side is your largest
12
00:00:46.539 --> 00:00:49.960 A:middle L:90%
angle. So by the Conn versus Hinge here,
13
00:00:49.960 --> 00:00:53.229 A:middle L:90%
um, we know that the angles 72 degrees must
14
00:00:53.229 --> 00:00:57.829 A:middle L:90%
be greater than to Z minus seven. Using some
15
00:00:57.840 --> 00:01:06.989 A:middle L:90%
algebra I get 79 is greater than to Z and
16
00:01:07.000 --> 00:01:17.140 A:middle L:90%
dividing by two we get Z is less than 79
17
00:01:17.140 --> 00:01:25.079 A:middle L:90%
over to, or we could say Z is less
18
00:01:25.079 --> 00:01:30.079 A:middle L:90%
than 39.5. However, this is not the only
19
00:01:30.079 --> 00:01:34.590 A:middle L:90%
condition we need to consider going back to Z being
20
00:01:34.590 --> 00:01:38.870 A:middle L:90%
a variable inside an unknown angle measure. What we
21
00:01:38.870 --> 00:01:42.010 A:middle L:90%
do know is that angle measured cannot equal zero.
22
00:01:42.010 --> 00:01:45.560 A:middle L:90%
It's gotta be greater than zero, so we have
23
00:01:45.569 --> 00:01:49.390 A:middle L:90%
to. Z minus seven is an angle measure and
24
00:01:49.390 --> 00:01:53.650 A:middle L:90%
that must be greater than zero. If I add
25
00:01:53.650 --> 00:01:57.409 A:middle L:90%
seven to both signs, I get to Z is
26
00:01:57.409 --> 00:02:05.140 A:middle L:90%
greater than seven and dividing by two I get Z
27
00:02:05.329 --> 00:02:12.080 A:middle L:90%
is greater than seven halves, or Z is greater
28
00:02:12.080 --> 00:02:19.750 A:middle L:90%
than 3.5. So to find our range of Z
29
00:02:19.759 --> 00:02:23.750 A:middle L:90%
, we will use all values of Z such that
30
00:02:24.639 --> 00:02:30.689 A:middle L:90%
3.5 is less than any Z value. But Z
31
00:02:30.689 --> 00:02:35.050 A:middle L:90%
is also less than 39.5.