True/False
All similar figures are rectilinear.
False
Circles can be similar, but they are not rectilinear.
AAA, SSS, and SAS
In triangle ABC, D is a point on AB and E a point on AC such that DE is parallel to BC. BC = 2x +1, DE = 5, AB = 2x -2, and AD = 4. What do we know about triangles ABC and ADE?
They are similar !
Chords AB and CD are drawn in a circle meeting at E. AB = 32, CE = 12, and ED = 5 (AE < EB). What equation do we set up in order to solve this (use line segment names)?
AE( EB ) = CE( ED )
How do we know we can join points?
Postulate 1
If 2 polygons are congruent, they are also similar.
True
All congruent figures are similar, however not all similar figures are congruent.
The areas of two triangles with the same height are in the same ratio as their __________.
In triangle ABC, D is a point on AB and E a point on AC such that DE is parallel to BC. BC = 2x +1, DE = 5, AB = 2x -2, and AD = 4. What do we need to set up to solve this problem?
A proportion using corresponding sides of the 2 triangles.
Chords AB and CD are drawn in a circle meeting at E. AB = 32, CE = 12, and ED = 5 (AE < EB). Using the previous equation, plug the necessary numbers into the equation.
x( 32 - x) = 12( 6 )
What does rectilinear mean?
No cyclic quadrilaterals are similar.
False
VI.31 generalizes the _____________ _______________ to all shapes similar and similarly situated on the sides of a right triangle.
Pythagorean Theorem
In triangle ABC, angle BAC has been bisected by AD, with D on side BC. AB = 2x -2, AC = 3x +4, BD = 4, and DC = 10. What is the name of the theorem needed to solve this problem?
Angle Bisector Theorem
Tangent TA meets circle ABC at A and secant TB meets the circle at B and C, such that TB > TC. BC = 4 and CT = 5. What equation do we need to set up in order to solve this problem?
TB( TC ) = TA2
What is the definition of similar figures?
Figures with equal angles and corresponding sides proportional.
If 2 quadrilaterals are equiangular, they are also similar.
False
2 triangles that are equiangular are similar, but we do not specifically know about quadrilaterals.
In the proportion a:b :: c:d, the terms a and d are called the ________________, while b and c are called the _______________.
1. Extremes
2. Means
In triangle ABC, angle BAC has been bisected by AD, with D on side BC. AB = 2x -2, AC = 3x +4, BD = 4, and DC = 10. What do we know about triangles ADC and BDA?
They are similar.
Tangent TA meets circle ABC at A and secant TB meets the circle at B and C, such that TB > TC. BC = 4 and CT = 5. Using the previous equation, plug the necessary numbers into the equation.
9( 5 ) = TA2
What proposition in book 1 has the steps to construct parallel lines?
I.31
Similar Figures are in the triplicate ratio of the ratio of their sides
False
Similar figures are in the duplicate ratio of the ratio of their sides.
A line drawn _____________ to the base of a triangle cuts the sides of the triangle proportionally.
parallel
This is the side splitter theorem from VI.2
In triangle ABC, angle BAC has been bisected by AD, with D on side BC. AB = 2x -2, AC = 3x +4, BD = 4, and DC = 10. What do we need to set up in order to solve this problem?
A proportion using corresponding sides of the 2 triangles.
Tangent TA meets circle ABC at A and secant TB meets the circle at B and C, such that TB > TC. If BC = 4 and CT = 5, find TA.
TA = 3*SQRT(5)
(1/2 credit): TA = SQRT(45)
In what proposition did we learn that triangles on the same base in the same parallels have equal areas?
I.38