Dilation & similarity
This specific term describes 2 triangles that possess identical corresponding angle measurements but proportional corresponding side lengths.
What is similar?
In a right triangle, the sine of an acute angle is defines as the length of the opposite side divided by the length of this side.
What is the hypotenuse?
This transformation type - which includes translations, reflection, and rotation - moves a triangle without changing its side lengths or angles.
What is a rigid motion?
This geometric formula, derived directly from the Pythagorean Theorem, is used to find the exact side lengths of a triangle on a coordinate plane.
This is the minimum number of matching congruent angles needed to mathematically prove two triangles are similar.
What is two? (Angle-Angle)
Because the two non-right angles in a right triangle add up to 90 degrees, the sine of one angle is always equal to this function of its complement.
This congruence theorem applies exclusively to right triangles, requiring only the longest side and one perpendicular leg to match.
What is HL?
To find the exact coordinates of a triangle's midsegment endpoints, you must apply this specific averaging formula to the vertices.
What is the Midpoint Formula?
Besides AA, there are the other two shorthand postures used to formally prove triangle similarity.
What are SAS and SSS similarity?
This is the specific trigonometric function you must use when you know two side lengths of a right triangle but need to calculate a missing interior angle measure.
What is an inverse trigonometric function?
According to the isosceles Triangle Theorem, if two sides of a triangle are congruent, the angles opposite those sides must possess this property.
What is congruent or equal?
If a triangle on a coordinate grid has vertices at (0,0), (8,0), and (4,6), it is classified as this type of triangle based on its side lengths.
What is a isosceles triangle?
When dilation transformation scales on a triangle down, this fixed point on the coordinate grid serves as the anchor from which all distances are shrunk.
Measured relative to a flat horizontal line of sight, this specific angle is used in word problems when your looking for building heights or a kite flying.
What is the angle of elevation?
This is the geometric justification behind why the angle-angle-angle (AAA) combination fails to prove that two triangles are congruent.
What is because it only proves similarity?
When dilating a triangle from the origin (0,0) by a scale factor of k, this is the coordinate rule applied to every original vertex (x,y)
What is (kx,ky)?
This theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, it cuts those two sides into proportional segments.
What is the Triangle Proportionality Theorem?
Drawing an altitude from the 90-degree vertex to the hypotenuse divides the original right triangle into two smaller triangles that have this relationship to each other.
What is similar?
This theorem states that a line segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half its length
What is the Triangle Midsegment Theorem?
On a coordinate grid, if triangle side A has a slope of 3 over 4 and side B has a slope of -4 over 3, this specific type of triangle is formed.
What is a right triangle?