H.Geometry – Chapter 11 – Definition Sheet

___

Review:

_________________________

_________________________

Solving Proportions

- An expression comparing two like quantities by division. Example: Female students to male students _________, ____________, ___________, __________

- The comparison of Unlike quantities. Example: _________________

Examples:

5

8=

𝑥

20

2𝑥−1

21=

𝑥−5

24

Similar Figures

- Have the ____________________ but not necessarily the

________________________. Examples: Models, blue prints, photography, etc. Which of these shapes are similar? All Rectangles? All Regular Pentagons? All Squares? All 30-60-90 Triangles? All Pentagons? All Circles?

Section 11.1

H.Geometry – Chapter 11 – Definition Sheet

Defintiion of Similar Polygons:

-Two polygons are similar if and only if:

(1) Corresponding Pairs of angles are _____________________________.

(2) Corresponding pairs of sides are ______________________________. (have the same ratio) *******BOTH PARTS MUST BE TRUE!!!!!

Symbol: _________________ Scale factor (k) = the ratio of the length of the sides.

H.Geometry – Chapter 11 – Definition Sheet

Re

Similar Polygons:

-Must have both of the following to be true: ____________________________________________ ____________________________________________

Congruent Triangle

Shortcuts:

-Ways of proving two triangles were congruent without having to know ALL of the sides AND angles.

Shortcuts: __________, __________,__________, __________, __________, __________

_____________

Similarity Conjecture

-If the _______________________ of one triangle is proportional to the _______ ____________ of another triangle, then the two triangles are _________________.

_____________

Similarity Conjecture

-If _______________________ of one triangle are congruent to ________________ of another triangle, then the two triangles are _________________. (3 pairs of _________ are automatically congruent… why?!)

Section 11.2

H.Geometry – Chapter 11 – Definition Sheet

_____________

Similarity Conjecture

-If _______________________ of one triangle are proportional to ________________ of another triangle AND INCLUDED ANGLES ARE __________________, then the two triangles are _________________. Note: There is NO SSA similarity conjecture -Why do we not need ASA or AAS similarity?

Example: Identify the similar triangles and explain why they are similar.

H.Geometry – Chapter 11 – Definition Sheet

Similar Triangles

- Can be used to find the measurements of otherwise measurable objects

Example: ____________________, ____________________, ___________________

Section 11.3

H.Geometry – Chapter 11 – Definition Sheet

H.Geometry – Chapter 11 – Definition Sheet

Recall:

_____________________

What about similar triangles?

-Corresponding Parts of Congruent Triangles are Congruent Corresponding angles? Corresponding Sides? What about other parts? Altitudes? Medians? Angle Bisectors?

Proportional Parts Conjecture

-If two triangles are similar, then any corresponding lengths (________________, ________________, ______________________ ______________________, etc.) are proportional to the corresponding sides. - This proportion is the same as the scale factor (k).

Section 11.4

H.Geometry – Chapter 11 – Definition Sheet

Angle Bisectors Proportions

Conjecture

- The angle bisector in a triangle divides the opposite sides into _______

segments whose lengths are in the same ratio as the length of the two sides forming the angle.

H.Geometry – Chapter 11 – Definition Sheet

What is true about the areas of similar figures?

Proportional Areas Conjecture

- If two similar figures have corresponing lengths in ration of 𝑎

𝑏 (i.e. the scale factor)

then the corresponding areas are in the ratio of: _______________ or __________ This applies to 3-D and 2-D figures!

Section 11.5

Section 7.5

H.Geometry – Chapter 11 – Definition Sheet

H.Geometry – Chapter 11 – Definition Sheet

H.Geometry – Chapter 11 – Definition Sheet

Similar Solids

- Have the same ___________ but not necessarily the same ____________ Example: Are these always similar? All speheres? All square pyramids? All Cubes? All Cylinders? All Cones? All Right Pentagonal Prisms? All Pyramids?

Similar Polyhedrons

- MUST HAVE: _________________________________________________________ _________________________________________________________ (ratio equals the scale factor)

Find the volumes of the two spheres: (k=3)

Section 11.6

Section 7.5

H.Geometry – Chapter 11 – Definition Sheet

Proportional Areas and

Volumes Conjecture

- If two similar figures have corresponding length in ratio of _______ (ie. The scale factor is k = _________) then: ***The corresponding areas are in ratio of _________ or _________ ____________________ *** The corresponding volumes are in ratio of _________ or _________ ____________________

H.Geometry – Chapter 11 – Definition Sheet

H.Geometry – Chapter 11 – Definition Sheet

0

Parallel/ Proportionality Conjecture

A) If a line ______________________ to one side of a triangle passes through the other two sides, then it divides the two sides __________________________________.

B) (Converse)

If a line cuts two sides of a triangle __________________________, then it is ___________________ to the third side

Section 11.7

Section 7.5

H.Geometry – Chapter 11 – Definition Sheet

H.Geometry – Chapter 11 – Definition Sheet

Extended Parallel

Proportionality Conjecture

- If two or more lines pass through two sides of a triangle are ________________ to the thrid side, then they divide the two sides _____________________________.