Triangle
What is the sum of the interior angles in any triangle?
180 degrees
What do you call angles that add up to 90 degrees?
Complementary angles
What is the term for two shapes that are identical in size and shape?
Congruent shapes
What is a scale factor in similar figures?
The ratio of the lengths of corresponding sides of similar figures.
What is a rigid transformation?
A transformation that preserves distance and angle measures, such as translation, rotation, or reflection.
State the Pythagorean theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides ((a^2 + b^2 = c^2)).
What do you call angles that add up to 180 degrees?
Supplementary angles
Name 2 methods used to prove triangles are congruent.
SSS (Side-Side-Side), SAS (Side-Angle-Side), or AAS (Angle-Angle-Side)
How do you determine if two triangles are similar?
By comparing their corresponding angles (AA criterion) or side ratios (SAS similarity).
What happens to a shape when it is translated?
The shape moves to a different position without changing its size or orientation.
State the isosceles triangle theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
If two angles are vertical angles, what is true about them?
Vertical angles are equal.
If two triangles are congruent, what can we say about their corresponding sides?
Their corresponding sides are equal in length.
If two triangles have a scale factor of 2, what does this mean?
Each side of the larger triangle is twice the length of the corresponding side of the smaller triangle.
What is the difference between a rotation and a reflection?
A rotation turns the shape around a point, while a reflection flips the shape over a line.
What is the relationship between the sides of similar triangles?
The ratios of the lengths of corresponding sides are equal.
What is the measurement of each angle in an equilateral triangle?
60 degrees
How can you determine if two angles are congruent?
If they have the same measure.
Name one real-world example of similar figures.
Maps and models (e.g., scale models of buildings).
Can you perform a rigid transformation on a shape and change its size?
No, rigid transformations do not change the size or shape of the figure.
State the converse of Thales theorem
If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side
How can you find the measurement of an exterior angle of a triangle?
The exterior angle is equal to the sum of the two opposite interior angles.
What is the relationship between congruence and rigid transformations?
Congruent shapes can be obtained from one another through rigid transformations (translations, rotations, reflections) without altering their size or shape.
If two similar triangles have a scale factor of 3:4, what is the ratio of their areas?
The ratio of their areas is (9:16) (the square of the scale factor).
Describe how to perform a reflection across the x-axis.
Each point on the shape is mapped to a point directly opposite it on the x-axis (y-coordinates change sign).