A point has position and no size; a moving point traces a line, and a moving line fills a plane.
The same two points can make a line that runs both ways, a ray that goes one way, or a segment that stops.
The opening between two rays is an angle, sorted as acute, right, or obtuse around a 90 degree corner.
Drag the angle slider and watch acute, right, obtuse, and straight take turns.
Point · Line · Ray · Segment
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Types of lines — line (both ways), ray (one way), segment (finite)
👀 Basic Geometric Elements
①Point: position only, no size
②Line: trace of a moving point (only length)
③Plane: trace of a moving line (only area)
④Distance between two points = length of the segment
⑤Line AB = line BA. Ray AB ≠ ray BA (direction differs). Segment AB = segment BA
Types of Angles
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Adjust the angle — acute · right · obtuse · straight (slider max 180° — reflex is not reachable here)
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🔍 Angle Categories
①Acute: 0° < θ < 90° (small, sharp)
②Right: exactly 90°
③Obtuse: 90° < θ < 180° (large, blunt)
④Straight: exactly 180° (a straight line)
Vertical, Complementary & Supplementary Angles
Vertical Angles
Opposite angles formed by two lines are equal
∠a = ∠c, ∠b = ∠d (vertical angles)
Complementary
∠A + ∠B = 90° → complementary
Sum of two angles is 90°
Supplementary
∠A + ∠B = 180° → supplementary
Sum of two angles is 180°
💡 Angle Relations Summary
①Vertical angles are always equal
②Adjacent angles sum to 180° (supplementary)
③Complementary = sum 90°; supplementary = sum 180°
④Complementary means two angles that sum to 90°. Do not write the complement of a right angle as 0°
Work It Out
Example 1
Two lines meet at a point; one angle is 65°. Find its vertical (opposite) angle.
1
Vertical angles are equal.
vertical angles are equal
2
So it equals the given angle.
∠x = 65°
▸ 65°
When two lines cross, opposite (vertical) angles are always equal.
Example 2
At a point on a line, two angles of sizes 3x and 2x form a straight angle. Find x.
1
A straight angle is 180°, so the two angles add to 180°.
3x + 2x = 180°
2
Simplify and solve for x.
5x = 180° ⇒ x = 36°
▸ x = 36°
Turn a straight angle (180°) or right angle (90°) into an equation.