# SPACE

### Malaka Shoukair

## Here are the rules that should be followed:

## A. Lines and planes

** 1. ****If two straight lines (d) and (d') of space are perpendicular to the same plane then they are parallel to each other.**

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**2. ****If a plane is perpendicular to a straight line (d) then all straight lines passing through a point B of the plane and perpendicular to (d) lie completely in the plane.**

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**3. ****The acute angle of a plane (P) and a straight line (d) is the angle where H is the orthogonal projection of any point A of (d) on (P).**

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**4. ****If a straight line (d) and plane (P) are perpendicular to the same line then they are parallel.**

**5. A straight line (d) is perpendicular to a plane (P) if and only if it is orthogonal to two intersecting lines of this plane.**

**( if a line(d) is perpendicular to a (P), then it is perpendicular to every line in (P))**

**6. if (l) perpendicular (d) and (d) contained in (Q)=> ****(l)perpendicular (Q)**

**when (l) perpendicular (Q)=> 1.(l) perpendicular (l') if (l') contained in (Q)**

** 2.(P) perpendicular (Q) if (l) contained in (P)**

## Common perpendicular

## B. Planes

## 2. Prove Two planes parallel

## C. Mediator plane of [AB]

**Proof:**

**1. Definition:**

**a plane perpendicular to a segment [AB] at its midpoint.**

**2.Proving 3 non-collinear points of a plane are equidistant to segment [AB]**

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## D. Axis

**Property: Any point on (d) is equidistant from any point on (C)**

**Proof axis:**

**1. **__Definition__**: (d) is axis of circle if (d) perpendicular (C) at O (center of (C))**

**2. ****A is a point on (d) and B,C,D are point on the circle prove: AB=AC=AD and**

**(AK) perpendicular (C) =>K center (AK) axis**

## REMARK:

**1. If a straight line (d) //(P) it doesn’t mean that (d) // to any line in (P)**

**2. Perpendicular( intersecting)**

** orthogonal (skew, not intersecting)**

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