Congruence
This type of triangle proof uses two sides and the angle between them.
What is SAS Congruence?
This transformation changes the size of a figure but keeps angles the same.
(What is a dilation?)
This formula finds the point halfway between two coordinates.
(What is the midpoint formula?)
This is the standard form of the equation of a circle.
(What is (x – h)² + (y – k)² = r²?)
A triangle is reflected over the x-axis and translated 4 units right. These two properties are preserved.
(What are angle measure and side length?)
These three rigid motions preserve congruence.
(What are translation, rotation, and reflection?)
These criteria prove two triangles are similar.
(What are AA, SSS, and SAS Similarity?)
This formula calculates the distance between two points.
(What is the distance formula?)
This part of the circle equation tells you the center.
(What are h and k in the equation?)
A mural includes a triangle (base 6 ft, height 8 ft) and a circle (radius 3 ft). This is the approximate total area.
(What is 52.27 ft²?)
These triangle congruence shortcuts do NOT prove congruence.
(What are SSA and AAA?)
A student thinks all transformations preserve size. This is false because of this transformation.
(What is a dilation?)
The slope between two points is –2. This is the slope of a line perpendicular to it.
(What is 1/2?)
This part of the circle equation determines the size of the circle.
(What is the radius?)
A student creates a right triangle with side lengths 7, 24, and 25. This property confirms it is a right triangle.
(What is the Pythagorean Theorem?)
This type of triangle congruence is only valid for right triangles.
(What is HL Congruence?)
A figure rotates 180° around the origin. This rule describes the transformation.
(What is (x, y) → (–x, –y)?)
The slope of a perpendicular line is this in relation to the original.
What is the opposite reciprocal?
A student is given the equation (x – 2)² + (y + 3)² = 25. This is the center and radius.
(What is center (2, –3) and radius 5?)
After applying a dilation with scale factor 1.5, the triangle’s perimeter changes in this way.
(What is it increases by a factor of 1.5?)
A student forgets to mark corresponding sides when comparing two triangles. This common mistake affects this part of a proof.
(What is the congruence statement?)
A sequence of transformations maps one triangle to another and preserves shape and size. This proves this relationship.
(What is congruence?)
A student plots three points but forgets to check collinearity. This is one method to check.
(What is using slope to verify all points lie on the same line?)
A student is asked to write the equation of a circle centered at the origin with a radius of 6. This is the correct equation.
(What is x² + y² = 36?)
A student is given coordinates and asked to verify a quadrilateral is a rectangle. These are the properties they must check.
(What are opposite sides equal, slopes of adjacent sides are negative reciprocals?)