KA Geometry Unit 4: Similarity

What are similar figures?

Figures with the same shape but possibly different sizes.

What transformations prove similarity?

Rigid motions and/or dilations.

What does similarity preserve?

Angle measures and side ratios.

Are congruent figures always similar?

Yes, congruent implies similarity.

How do you solve 8/10 = 6/m?

Cross multiply: 8m = 60 → m = 7.5.

What is the strategy to solve proportions?

Multiply both sides by the product of denominators.

What's the solution to x + 19 - x = 23?

x = 3 (after simplifying and solving).

What should you do first in rational equations?

Clear denominators and combine like terms.

What is triangle similarity?

Triangles with same shape, different size.

What do similar triangles have?

Equal angles, proportional sides.

What are the triangle similarity postulates?

AA, SSS, SAS.

What does AA postulate state?

Two equal angles prove similarity.

What does SSS postulate state?

All sides in the same ratio.

What does SAS postulate state?

Two proportional sides and included equal angle.

Do we need ASA or AAS for similarity?

No, AA is enough for similarity.

What must be proven before solving?

That triangles are similar.

How do you solve for missing sides?

Set up ratios of corresponding sides.

What’s the formula for solving with similar triangles?

side1 / total1 = side2 / total2.

Solve: 5/8 = 4/CE → CE = ?

CE = 32/5.

Solve: 8/BC = BC/2 → BC = ?

BC = 4.

What’s the equation setup?

AC/BC = BC/DC.

What does the Angle Bisector Theorem state?

AB/AC = BD/DC.

What does the angle bisector do?

Divides opposite side into segments proportional to adjacent sides.

Solve: 12/18 = 6/x → x = ?

x = 9.

What’s key to setting up ratios in angle bisector problems?

Keep consistent directions from the vertex.

What formula is used for modeling with similar triangles?

side1/total1 = side2/total2.

What are congruent triangles?

Triangles that are identical in size and shape.

What’s one method to prove triangle relationships?

Show similarity using AA, SAS, or SSS.

What’s the golden ratio?

Approximately 1.61803….