IDLA Geometry A terms

Lakukan tugas rumah & ujian kamu dengan baik sekarang menggunakan Quizwiz!

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.


Set pelajaran terkait

Chapter 5 - Maximizing Your Memory & Mastering Tests Quiz

View Set

health and nutrition: lacto-ovo-vegetarian diet

View Set

ANA Scope and Standards of Practice

View Set

Chapter 68: Emergency and Disaster Nursing Lewis: Medical-Surgical Nursing, 10th Edition ?'s

View Set