Download Exterior Angle Theorem and Angle

Name: _____________________________
Geometry
Date: ____________
Do – Now: Find the value of x
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Exterior Angle Theorem and Angle-Side Relationships
Exterior Angle Theorem and An Inequality Involving the Exterior Angle Theorem
The exterior angle theorem states that ____________________
Therefore, the measure of an exterior angle must be greater
than the measure of either nonadjacent interior angles.
Ex:
Examples: #1 and 2, use diagram to the right.
1) Name all angles whose measures must be less than m<7.
2) Name all angles whose measures must be greater than m<6.
3) Solve for x.
4) Solve for x.
Angle Side Relationships in Triangles:
Theorem
Picture
If one side of a triangle is
longer than another side, than
the angle opposite the longer
side is greater in measure
than the angle opposite the
shorter side.
If one angle of a triangle is
greater in measure than
another angle, then the side
opposite the larger angle is
longer than the sure opposite
the smaller angle.
Examples:
1) List the angles in order from shortest to longest.
2) List the sides in order from shortest to longest.
a)
3) Which is the longest side of
b)
?
Explanation
Name: ______________________
Homework: Exterior Angle Theorem and Angle-Side Relationships in Triangles
1)
Solve for x and j.
2) In the diagram below of
. What is
3) In the diagram below of
, side
is extended to point D,
,
, and
?
, side
is extended to point A. Which statement must be true?
1)
2)
3)
4)
4) In scalene triangle ABC,
longest to shortest?
1)
,
,
2)
,
,
3)
,
,
4)
,
,
and
. What is the order of the sides in length, from
5) As shown in the diagram below,
, and
is a diagonal of trapezoid STAR,
. Determine and state the longest side of
,
.
Some Review…
6) Solve for g.
7) Solve for h.
,