Intro to Triangles
Today you will need:
Grab a warm-up off the wooden desk and get started! :-)
Goals:
Warm-up #1
Warm-up #2
Warm-up #1
Perform the following composition of transformations:
Rotate 90 degrees about the origin
Translate (x-3, y+5)
Reflect over the y-axis
Warm-up #2
What is the scale factor? Is the dilation an enlargement or a reduction?
How do you find the scale factor?
Center of Dilation to Image
Center of Dilation to Preimage
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Classifying Triangles by Sides
Scalene Triangle | Isosceles Triangle | Equilateral Triangle |
Classifying Triangles by Angles
Acute Triangle all angles < 90 | Right Triangle 1 right angle. | Obtuse Triangle biggest angle > 90 | Equiangular Triangle All angles = 60 |
Classify by angle measure
Obtuse - biggest angle > 90
Acute - all angles < 90
Right - 1 right angle.
NEW THEOREMS | Description | Picture |
Triangle Sum Theorem | The sum of the measures of the interior angles of a triangle is 180 degrees. | |
Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. | |
Corollary to the Triangle Sum Theorem | The acute angles of a right triangle are complementary. | |
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Resources
Mod 4 Standards
G.CO.10 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motion.
G.CO.11 Prove and apply theorems about parallelograms. Theorems include but are not restricted to the following: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Warm-up: Kahoot!