standard_description: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
problem_activity: Problem 1
Your group should have a few copies of
Handout #2
and a set of cards from
Handout #1
.
Draw three cards and place them in the appropriate places on the Handout #2 form. This represents three conditions about a triangle. Once you’ve placed them on the form, do not change the order.
Determine if the set of conditions will make one unique triangle, more than one triangle, or no triangle.
If you can make one unique triangle, draw and label the triangle.
If more than one or no triangle can be made, be prepared to explain your reasoning.
Choose another three cards and repeat the activity.
Problem 2
Two triangles are described below. Determine if each description results in one unique triangle, more than one triangle, or no triangle. Explain your reasoning or draw images to support your conclusion.
a.   Triangle
$${EFG}$$
is an isosceles triangle with two angles measuring 35°. Side length
$${EG}$$
measures 10 cm.
b.   Triangle
$${{PQ}R}$$
is an isosceles triangle with
$${\angle P}$$
and
$${\angle Q}$$
measuring 22°. Side length
$${PQ}$$
measures 8 cm.


aligns: no