NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There...
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Transcript of NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There...
![Page 1: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/1.jpg)
![Page 2: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/2.jpg)
NO NEED TO COPY
Recall from 5-1 that an isosceles triangle has at least two congruent sides.
There are two theorems dealing with isosceles triangles
![Page 3: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/3.jpg)
THEOREM 6-2: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
![Page 4: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/4.jpg)
THEOREM 6-3: The median from the vertex angle of an isosceles triangle IS ALSO the perpendicular bisector of the base AND IS ALSO the angle bisector of the vertex angle.
![Page 5: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/5.jpg)
Example Find the value of each variable in isosceles
triangle DEF if EG is an angle bisector.▪ Ignore the bisector for a
second…▪ This is an isosceles triangle▪ Angles opposite equal sides are
equal▪ x = 49
▪ Bring the bisector back in▪ The angle bisector of an isosceles triangle is also the
perpendicular bisector▪ y = 90
![Page 6: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/6.jpg)
YOUR TURN Find the value of the variables in each
triangle
x = 65˚y = 50˚
x = 90˚y = 70˚
![Page 7: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/7.jpg)
THEOREM 6-4: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
![Page 8: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/8.jpg)
Example In ABC, A B and mA = 48. Find mC, AC, and BC.▪ Finding mC▪ A B, so B also equals 48.▪ 180˚ in a triangle.▪ 48 + 48 + C = 180▪ 96 + C = 180▪ C = 84
![Page 9: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/9.jpg)
Example In ABC, A B and mA = 48. Find mC, AC, and BC.▪ Finding AC & BC▪ This is an isosceles triangle, so
the two marked sides are equal.▪ 4x = 6x – 5▪ -2x = -5
▪ x = 5/2 (or 2.5)
▪ Plug back in to get AC/BC▪ AC = 4(2.5) = 10 BC = 6(2.5) – 5 = 10
![Page 10: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/10.jpg)
THEOREM 6-5: A triangle is only equilateral if it is equiangular
![Page 11: NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles.](https://reader036.fdocuments.us/reader036/viewer/2022083008/56649f255503460f94c3bd35/html5/thumbnails/11.jpg)
Assignment Study Guide #6-4 and
Practice Masters #6-4