Download Advanced Geometry LT 3.1 Isosceles Triangles

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Transcript
Advanced Geometry
LT 3.1 Isosceles Triangles
Parts of an Isosceles Triangle
Use the diagram to the right to fill in the blanks:
The congruent sides are called the ______ of the triangle.
The angle formed by the legs is the _______________.
The side opposite the vertex angle is the _________.
The angles that have the base as a side are the ___________________.
Isosceles Triangle Theorem
Two sides of a triangle are congruent if and only if the angles opposite them are congruent.
Reflect:
1. Using the proper names from above, which parts will be congruent in an isosceles triangle?
2. Restate the Isosceles Triangle Theorem in your own words so that you will remember it.
3. Consider the vertex and base angles of an isosceles triangle. Can they be right angles? Can they be obtuse?
Explain.
4. Error Analysis: Two students are asked to find the angle measures of
Their work is shown below. Is either answer incorrect? Explain.
, given that
is isosceles.
Practice:
Find the measure of the indicated angle.
1.
2.
3.
4.
5.
6.
Find the length of the indicated side.
7.
8.
9.
10. Given
with
and
, is the triangle a scalene, isosceles, equilateral, acute, obtuse
or right triangle? List all that apply and justify your answer.
11. The control tower at airport A is in contact with an airplane flying at point P, when it is 5 miles from the
airport, and 30 seconds later when it is at point Q, 4 miles from the airport. The diagram shows the angles that
the plane makes with the ground at both times. If the plane flies parallel to the ground from P to Q at a constant
speed, how fast is it travelling?