ENTRY TASK – TWO LEVELS Medium/Difficult

Given: ACB EDB and ∠ ∠Prove: ΔABC ΔEBD

Given: ACB EDB and ∠ ∠Prove: ΔAFD ΔEFC

F

DilationA dilation is a transformation that enlarges or reduces an image proportionally. The corresponding angles are congruent, but the corresponding sides are proportional. NOTE: This is the first and only transformation that we have that is not an isometry. Instead of producing an image that is congruent to the pre-image, it produces one that is similar (same shape, but different size.)

factor of .5

How would we do this using a compass and straight edge?

What is the center of dilation? What is the scale factor? (Is it pre-image over image or the other way around? WHY?

What is the center of dilation? And what is the scale factor?

is a dilation image of with center of dilation X. • Is the dilation an enlargement or reduction?• What is the scale factor? (Careful. This one is a little bit tricky!)

Dilate ΔZPG with center of dilation (0,0) and scale factor of 2.

Transformations

• Rotation – Need Center, degrees of rotation and direction• Reflection –Need a line of reflection• Translation – Need a vector, or an amount left or right, up or down.• Glide Reflection – Combine reflection and translation• Dilation – Need center and scale factor.

• Which of these is not an isometry?

Quiz Review

Quiz will cover • Special points of concurrency• Incenter, Circumcenter, Orthocenter, Centroid

• Special Segments in Triangles• Midsegment, median, altitude, angle bisectors, perpendicular bisectors

• Overlapping Triangle Proofs• Inequalities in Triangles

White board Practice

Resource Manager grab a white board, marker and eraser for each person in your group.

What is this a picture of?

The intersection of the altitudes is the …..

The intersection of the medians is the …..

The intersection of the angle bisectors is the ….

The intersection of the perpendicular bisectors is the …..

If a triangle has side lengths 3 and 16, what is the possible range of lengths for the third side?

Will the following side lengths form a Triangle?• 3, 4, 5• 10, 10, 10• 6, 7, 13• 3, 5, 9

List the sides from shortest to longest.

List the sides from shortest to longest.

List the angles from largest to smallest

List the angles from largest to smallest

In ΔRST, U is the centroid.

1.) If UQ is 6, find US and QS.2.) If UT is 3, find UV and TV. 3.) If UW =2, find UR and WR.

FIND the value of x.

FIND X

FIND THE VALUE OF X.

Assignment Page 578 #1, 2, 6, 12, 14, 16