Dilations
dilate the following triangle by a scale factor of 2 use the origin as the center of dilation A(1,1) B(3,1) C (2,3)
what is 8
what is SSS
Two triangles are similar if all three pairs of corresponding sides are in the same ratio
This postulate is the most common way to prove two triangles are similar; it only requires checking two pairs of angles
What is AA
This is the first step in almost every geometry proof,
What are the Givens
The points where a midsegment connects to the triangle sides are called this
What are midpoints?
Dilate the following triangle by a scale factor of 0.5 use the origin as the center of dilation A(2,2) B(4,6) C(8,2)
What is A(1,1) B(2,3) C(4,1)
While similar figures can have different side lengths, these internal measurements must always be congruent (equal).
What are Corresponding Angles
This postulate states that two planes intersect in this figure.
What is a line
In coordinate geometry proofs, this formula is used to prove that two segments are congruent.
What is the Distance Formula
In a triangle with a base of 24 inches, this would be the length of the corresponding midsegment.
what is 12 inches
To find the new coordinates of a point after a dilation centered at the origin, you must multiply both coordinates by this.
What is the scale factor (k)
Triangle ABC has sides 3, 4, 5. Triangle DEF has sides 9, 12, 15. Name the similarity theorem that proves they are similar.
What is SSS? (Scale factor is 3)
if 2 sides proportional & included angle congruent what is postulate
what is SAS
what are the three different ways to prove that two triangles are similar
AA,SAS,SSS
This geometric relationship describes the midsection and the third side, ensuring they never intersect.
what is parallel
A dilation with a scale factor k such that 0<k<1 is known by this term
what is reduction
: A 5-foot-4-inch woman casts a 40-inch shadow. If a nearby flagpole casts a 50-foot shadow, this is the height of the pole.
What is 80 Feet
if all sides are proportional, what's the postulate
what is SSS
This property, often used in proofs involving overlapping triangles, states that a side or angle is equal to itself (AB=AB)
What is the Reflexive Property?
If a triangle has a midsegment measuring 8 units, this is the length of the side it is parallel to
What is 16 units
If a square with an area of 4 cm² is dilated by a scale factor of 3, this is the area of the new square.
What is 36 cm²?
This type of transformation changes the size of a figure but keeps its shape the same.
What is a dilation
Opposite rays form this type of angle that measures 180°.
What is a straight angle
In a two-column proof, this is the left column where each step is written in order.
What are statements
f one side of a triangle is 14 units, the midsegment parallel to it will be this length.
What is 7 units