MUST KNOW GEOMETRY - Chapter 5 - SIMILARITY

When two triangles are similar, their corresponding A) angles are congruent and their corresponding sides are in proportion B) they are pretty together C) angles are in proportion and their corresponding sides are same in length

A) angles are congruent and their corresponding sides are in proportion

When a parallel line is drawn in a triangle it creates a smaller triangle within the large one. The three angles of the smaller triangle then are: A) congruent to the three angles in the big triangle B) similar to the three angles in the big triangle C) are completely different from the angles in the big triangle

A) congruent to the three angles in the big triangle

We use the order of the vertices in the names of the triangles to: A) determine angles correspond to one another B) to please mom C) to be more organized

A) determine angles correspond to one another

Dilations preserve angle measure but: A) not distance B) are tricky C) only for circles

A) not distance

When an altitude is drawn in a right triangle from the right angle to the hypotenuse, it forms: A) three similar right triangles B) three similar obtuse triangles C) three congruent triangles

A) three similar right triangles

Midsegment of a triangle is created when: A) when the midpoints of two sides of a triangle of a triangle are connected B) a line is drawn parallel to the third side at any points C) when a line is drawn from the vertex to the midpoint of the base

A) when the midpoints of two sides of a triangle of a triangle are connected

The parallel lines inside a triangle create congruent ______________________ A) waves B) corresponding angles C) corresponding midpoints

B) corresponding angles

The midsegment of a triangle is ______________________ to the third side of the triangle, and is _______________ of the length of the third side. A) perpendicular / one-third of the area of the triangle B) parallel / one-half of the length of the third side C) parallel / one-eight of the perimeter of the triangle

B) parallel / one-half of the length of the third side

If in triangles 🔺ABC and 🔺DEF AB/DE = 1/2 BC/EF = 1/2 AC/DF = 1/2 then the two triangles are: A) right triangles B) similar C) corresponding

B) similar

When a line is drawn inside a triangle and it is parallel to the side of the triangle, it creates: A) congruent triangles B) similar triangles C) obtuse triangles

B) similar triangles

Similarity occurs when we: A) draw figures by hand B) rotate polygons around C) dilate polygons

C) dilate polygons

When we talk about polygons being similar, we are saying that the polygons ________________________ A) have sides that are the same B) have almost the same sides and angles C) have maintained the same shape but not equal in size

C) have maintained the same shape but not equal in size

The ratio of areas of similar triangles IS NOT EQUAL to the: A) ratio of the perimeter B) ratio of the corresponding angles C) ratio of the corresponding sides

C) ratio of the corresponding sides

Similarity of triangles means _______________________ A) they are almost congruent B) almost the same C) they are alike but not identical

C) they are alike but not identical

The ratio of areas of similar triangles IS EQUAL to the: A) the square of the ratio of the perimeter B) the cube of the ratio of the corresponding angles C) to the square of the ratio of the corresponding sides

C) to the square of the ratio of the corresponding sides

There are many proportions that could be set up in triangles, just remember to: A) name the parts of the polygons B) keep all corresponding parts in order within the proportions C) keep order to all proportions D) all of the above

D) all of the above

Side Splitter Theorem

If a line or line segment intersecting two sides of the triangle is drawn parallel to the third side of the triangle, then NOT ONLY are the two triangles similar but the line will divide the segment of the two sides of the triangle proportionally.

What is the formula for the proportion between the projection and the leg of the right triangle?

Projection/Leg = Leg/Hypotenuse

One Proportion with corresponding sides of triangles involved the altitude from the right angle to the hypotenuse. What is the formula for that proportion?

Segment of Hypotenuse/Altitude = Altitude/ Other Segment of the Hypotenuse

Side-Angle-Side (SAS) Similarity Theorem

States that if two pairs of corresponding sides are in proportion and the included angles between these sides are congruent, then triangles are similar.

What is a projection in a right triangle?

This is the section or segment of the hypotenuse that is closest to the LEG of the right triangle.

Side-Side-Side (SSS) Similarity Theorem

This method states that if the three pairs of corresponding sides of a triangle are in proportion, then the triangles are similar.

Angle Angle Angle (AAA) Theorem

This theorem states that if three angles of the triangle are congruent to three corresponding angles in another triangle, the triangles are congruent

Similar triangles have ____________________

corresponding angles that are equal in measure and corresponding sides that are in proportion

In a proportion the first numerator and the second denominator are called

extremes

Critically important property of similar triangles parameters:

if two triangles are similar, then the ratio of the perimeters of the similar triangles is equal to the ratio of the corresponding sides of the similar triangles.

When an altitude is drawn to the hypotenuse of a right triangle _______________________

it forms three (3) similar right triangles

In a proportion the first denominator and second numerator are called

means

When you cross multiply the extremes and means , you can see that in a proportion ___________________

the product of the means is equal to the product of the extremes. extreme/mean = mean/extreme extreme^2 = mean^2

The Angle Angle Angle Theorem allows us _______________________

to prove triangles are similar