entry task – two levels medium/difficult f. dilation a dilation is a transformation that enlarges...
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/1.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/2.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/3.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/4.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/5.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/6.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/7.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/8.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/9.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/10.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/11.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/12.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/13.jpg)
![Page 14: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/14.jpg)
![Page 15: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/15.jpg)
![Page 16: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/16.jpg)
![Page 17: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/17.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/18.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/19.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/20.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/21.jpg)
![Page 22: ENTRY TASK – TWO LEVELS Medium/Difficult F. Dilation A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/22.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/23.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/24.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/25.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/26.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/27.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/28.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/29.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/30.jpg)
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](https://reader034.vdocuments.site/reader034/viewer/2022051622/5697c01f1a28abf838cd1dec/html5/thumbnails/31.jpg)
Assignment Page 578 #1, 2, 6, 12, 14, 16