entry task – two levels medium/difficult f. dilation a dilation is a transformation that enlarges...

31
ENTRY TASK – TWO LEVELS Medium/Difficult Given: ∠ACB ∠EDB and Prove: ΔABC ΔEBD Given: ∠ACB ∠EDB and Prove: ΔAFD ΔEFC F

Upload: judith-greene

Post on 21-Jan-2016

217 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

ENTRY TASK – TWO LEVELS Medium/Difficult

Given: ACB EDB and ∠ ∠Prove: ΔABC ΔEBD

Given: ACB EDB and ∠ ∠Prove: ΔAFD ΔEFC

F

Page 2: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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.)

Page 3: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

factor of .5

Page 4: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 5: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 6: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 7: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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!)

Page 8: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 9: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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?

Page 10: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 11: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

White board Practice

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

Page 12: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

What is this a picture of?

Page 13: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding
Page 14: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding
Page 15: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding
Page 16: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding
Page 17: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

The intersection of the altitudes is the …..

Page 18: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

The intersection of the medians is the …..

Page 19: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

The intersection of the angle bisectors is the ….

Page 20: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

The intersection of the perpendicular bisectors is the …..

Page 21: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding
Page 22: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 23: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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

Page 24: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

List the sides from shortest to longest.

Page 25: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

List the sides from shortest to longest.

Page 26: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

List the angles from largest to smallest

Page 27: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

List the angles from largest to smallest

Page 28: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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.

Page 29: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

FIND the value of x.

FIND X

Page 30: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

FIND THE VALUE OF X.

Page 31: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding

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