Triangles. If the dimensions of the corresponding sides of two **triangles** are proportional, then the **triangles** are **similar**. Likewise, if the dimensions of two sides in one triangle are proportional to the corresponding sides in another triangle and the enclosing **angles** are congruent, then the **triangles** are **similar**.

Just like that, are **parallel lines similar**?

Parallel Lines and Similar and Congruent Triangles

Theorem 6.1: When two **parallel lines** are intersected by a third, the alternating interior **angles** are equal. Theorem 6.2: If a line intersects two other **lines**, then the following conditions are equivalent. a) The alternating interior **angles** are equal.

And what are **similar** examples of **triangles**?

In **similar triangles**, corresponding sides always have the same ratio. For example: The **triangles** R and S are **similar**. The same **angles** are marked with the same number of arcs.

Also to know, how do you prove that **triangles** in **similar triangles** are **parallel**?

Answer: The side splitter theorem says that, if a line is **parallel** to one side of a triangle and the line intersects the other two sides, that line divides those two sides proportionally.

Are **parallel lines** congruent?

If two **parallel lines** are intersected by a transversal, the **corresponding angles** are congruent. If two **lines** are intersected by a transversal and the **corresponding angles** are congruent, the **lines** are **parallel**. Interior **angles** on the same side of the transverse line: The name is a description of the “location” of these **angles**.

## What do parallel lines mean?

Parallel **lines** are two **lines** that are always the same distance apart are and never touch. For two **lines** to be **parallel**, they must be drawn in the same plane, a perfectly flat surface like a wall or piece of paper. Any line that has the same slope as the original will never intersect with it.

## How do you prove parallelism?

The first is whether the **corresponding angles**, the **angles** , which are equal at each intersection on the are the same corner, then the **lines** are **parallel**. The second is when the alternating interior **angles**, the **angles** that are on opposite sides of the transversal and inside the **parallel lines**, are equal, then the **lines** are **parallel**.

## What are corresponding angles in triangles?

When two **lines** are crossed by another line (called a transverse line), the **angles** in matching corners are called **corresponding angles**. Example: a and e are **corresponding angles**. If the two **lines** are **parallel**, **corresponding angles** are equal.

## Which angles are congruent?

Congruent **angles** are two or more **angles** that have the same measure. In simple terms, they have the same number of degrees. It is important to note that the length of the edges of the **angles** or the direction of the **angles** does not affect their congruence. As long as their measure is the same, the **angles** are considered congruent.

## What is the Cpctc theorem?

CPCTC is an acronym for corresponding parts of congruent **triangles** are congruent. CPCTC is commonly used at or near the end of a proof that asks the student to show that two **angles** or two sides are congruent. Corresponding means they are in the same position in the 2 **triangles**.

## Are all congruent triangles similar?

Note that for **triangles** to be **similar**, only all **angles** are equal have to be . But for **triangles** to be cogruent, both **angles** and sides must be equal. So while congruent **triangles** are **similar**, **similar triangles** may not be congruent.

## Are all isosceles triangles similar?

Answer and Explanation:. No, all isosceles **triangles** are not **similar**. An isosceles triangle is a triangle with two sides of equal length.

## What are congruent triangles?

Congruent **triangles**. When two **triangles** are congruent, they have exactly the same three sides and exactly the same three **angles**. The same sides and **angles** may not be in the same position (when rotating or flipping), but they are there.

## What is the perpendicular symbol?

The ⊥ symbol

## How do you know if points are parallel?

To find out if 2 **lines** are **parallel**, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates and then substituting those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both **lines**. If they are equal, then the **lines** are **parallel**.

## What are the properties of parallel lines?

if the pair of **corresponding angles** are equal, then the two straight **lines** are **parallel** to each other. the pair of alternating **angles** is equal, then the two **lines** are **parallel** to each other. add the pair of interior **angles** on the same side of the transverse axis, then the two **lines** are **parallel**.

## How to tell if triangles are congruent?

Two **triangles** are congruent if they have: exactly the same three sides and. exactly the same three **angles**. There are five ways to find out if two **triangles** are congruent: SSS, SAS, ASA, AAS, and HL.

- SSS (side, side, side)
- SAS (side,
**angle**, side) - ASA (
**angle**, side,**angle**) - AAS (
**angle**,**angle**, side) - HL (hypotenuse, leg)

## What is the formula for similar triangles?

Ratio and Proportions – Similar Numbers – Detailed. If two objects have the same shape, they are said to be “**similar**“. When two figures are **similar**, the aspect ratios of their respective sides are the same. To determine if the **triangles** shown are **similar**, compare their corresponding sides.

## What types of triangles are always similar?

Isosceles **triangles** are not always **similar**, but equilateral **triangles** are always **similar**.

## What do you call it when two triangles share a side?

To be congruent, two **triangles** must have the same shape and size. However, they can share a side, and as long as they are otherwise identical, the **triangles** are still congruent.

## What do angles add to parallels?

Angles and parallels. When two **lines** intersect, they form two pairs of opposite **angles**, A + C and B + D. Another word for opposite **angles** is vertical **angles**. Two **angles** are said to be complementary if the sum of the two **angles** is 180°.

## What is the SAS Similarity Theorem?

SAS Similarity Theorem: When an **angle** of a triangle is congruent to the **corresponding angles** of another triangle and the lengths of the sides including those **angles** are proportional, then the **triangles** are **similar**.