IDLA Geometry A terms
Scale Drawing
A depiction of a real object with accurate sizes except they have all been reduced or enlarged.
Congruent angles, proportional sides
All similar triangles have ______ ______ and ________ _______.
Proportional
Corresponding sides of two similar triangles.
Similar Polygons
Figures that have congruent angles and corresponding sides that are proportional to one another.
Reflexive Property
For real number n, n=n.
Cross Product Property
For real numbers a, b, c, and d (where b and d cannot equal zero), a/b = c/d is equivalent to a • d = b • c or ad = bc.
Similar polygons are polygons that have CONGRUENT ANGLES and CORRESPONDING SIDES that are proportional to one another.
How do you determine if polygons are similar?
Angle-Angle (AA) Similarity Postulate
How do you determine if two triangles are similar? By using the...
A minimum of two congruent corresponding angles.
How many congruent corresponding angles are needed to prove two triangles are similar?
Converse of Triangle Proportionality Theorem
If a line divides any two sides of a triangle proportionally, then the line must be parallel to the third side.
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and also intersect the other two sides, the line divides the sides proportionally.
Pythagorean Theorem
If a right triangle has sides a and b and hypotenuse c, then a2 + b2 = c2
Corresponding Angles Postulate
If a transversal intersects two parallel lines, then the angles in the same location relative to the parallel lines and transversal are congruent.
Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then the angles inside the two parallel lines and on either side of the transversal are congruent.
Pythagorean Theorem
If a triangle has a right angle, then the sum of the squares of the shorter sides is equal to the square of the longest side. Or, given right triangle ABC, c² = a² + b², where c is the hypotenuse, while a and b are the two legs.
Pieces of Right Triangle Similarity Theorem
If an altitude is drawn from the right angle of a right triangle, the two smaller triangles created are similar to one another and to the larger triangle.
Converse of the Pythagorean Theorem
If the sum of the squares of the shorter sides is equal to the square of the longest side, then the triangle has a right angle. Or, given c² = a² + b², where a, b, and c are the sides of a triangle, the triangle is a right triangle.
Angle-Angle (AA) Similarity Postulate
If two corresponding angles of two or more triangles are congruent, then the triangles are similar.
Congruent
If two figures are similar, the resulting corresponding angles are always ______.
Side-Angle-Side Similarity postulate
If two or more triangles have corresponding, congruent angles, and the sides that create these angles are proportional, then the triangles are similar.
Side-Side-Side Similarity Postulate
If two or more triangles have three corresponding, proportional sides, then the triangles are similar.
Same shape, sizes
Similar polygons have the _____ _____ but different ________.
Corresponding, proportion, corresponding sides.
Similar triangles have ________ parts that form a _________ with their _________ ________.
Scale Factor
The constant by which a figure (or the dimensions of a figure) increases or decreases.
Corresponding angles
These corresponding parts are congruent, given two similar triangles.
Two pairs of corresponding angles
Triangle ABC has been dilated to form triangle DEF. What is the least amount of information needed to prove the two triangles are similar?
Corresponding angles of similar polygons ill always have congruent measures.
What relationships are formed by corresponding angles of similar polygons?
Each pair of corresponding sides of similar polygons will have equal ratios.
What relationships are formed by corresponding sides of similar polygons?
Proportional
When two fractions equal to one another.
