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Geom Gr7 > sec 2 > Flashcards

sec 2 Flashcards

geom (70 cards)

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1
Q

What is a straight line?

A

A line that extends infinitely in both directions.

Symbol: ←———→

Example: A horizon line

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2
Q

What is a line segment?

A

A part of a line with two endpoints.

Symbol: A———B

Example: The side of a triangle

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3
Q

What is a ray?

A

A part of a line with one endpoint that extends
infinitely in one direction.

Symbol: A———→

Example: A light beam from a torch

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4
Q

What are parallel lines?

A

Lines in the same plane that never meet
and are always the same distance apart.

Symbol: ∥

Example: Railway tracks

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5
Q

What are perpendicular lines?

A

Lines that meet at a right angle (90°).

Symbol: ⊥

Example: The corner of a page

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6
Q

What is an acute angle?

A

An angle that measures less than 90°.

Example: 45° is an acute angle.

Visual: ∠ (with a small opening)

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7
Q

What is a right angle?

A

An angle that measures exactly 90°.

Symbol: ⊥ or ∟

Example: The corner of a square

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8
Q

What is an obtuse angle?

A

An angle that measures more than 90° but less than 180°.

Example: 120° is an obtuse angle.

Visual: ∠ (with a wide opening)

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9
Q

What is a straight angle?

A

An angle that measures exactly 180°.

Example: A straight line forms a straight angle.

Visual: ——

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10
Q

What is a reflex angle?

A

An angle that measures more than 180° but less than 360°.

Example: 270° is a reflex angle.

Visual: The larger part of a circle when a smaller angle is formed

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11
Q

What are complementary angles?

A

Two angles whose sum equals 90°.

Example: 30° and 60° are complementary angles
because 30° + 60° = 90°

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12
Q

What are supplementary angles?

A

Two angles whose sum equals 180°.

Example: 45° and 135° are supplementary angles
because 45° + 135° = 180°

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13
Q

What are vertically opposite angles?

A

Pairs of opposite angles formed when two straight
lines intersect. Vertically opposite angles are equal.

Visual: When lines form an X, the opposite
angles are equal

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14
Q

What is the sum of angles on a straight line?

A

180°

Example: If one angle is 65°, the other angle
on the same straight line is 115° (180° - 65° = 115°)

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15
Q

What is the sum of angles around a point?

A

360°

Example: If three angles around a point are 90°, 120°,
and x°, then x = 150° (360° - 90° - 120° = 150°)

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16
Q

What are corresponding angles?

A

When a transversal crosses two parallel lines,
corresponding angles are in the same position
relative to each parallel line and the transversal.

Corresponding angles are EQUAL.

Visual: Use the F-pattern to identify them

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17
Q

What are alternate angles?

A

When a transversal crosses two parallel lines,
alternate angles are on opposite sides of the
transversal and between the parallel lines.

Alternate angles are EQUAL.

Visual: Use the Z-pattern to identify them

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18
Q

What are co-interior angles?

A

When a transversal crosses two parallel lines,
co-interior angles are on the same side of the
transversal and between the parallel lines.

Co-interior angles SUM TO 180°.

Visual: Use the C-pattern to identify them

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19
Q

What is an equilateral triangle?

A

A triangle with all three sides equal in length
and all three angles equal (60° each).

Properties:
- All sides equal
- All angles equal (60°)
- Three lines of symmetry

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20
Q

What is an isosceles triangle?

A

A triangle with two sides equal in length
and two angles equal.

Properties:
- Two sides equal
- Two angles equal (the base angles)
- One line of symmetry

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21
Q

What is a scalene triangle?

A

A triangle with no sides equal in length
and no angles equal.

Properties:
- All sides different lengths
- All angles different measures
- No lines of symmetry

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22
Q

What is an acute triangle?

A

A triangle with all three angles measuring less than 90°.

Example: A triangle with angles 60°, 60°, and 60°

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23
Q

What is a right-angled triangle?

A

A triangle with one angle measuring exactly 90°.

Properties:
- Pythagoras’ theorem applies
- The longest side (opposite the right angle) is the hypotenuse

Example: A triangle with angles 90°, 45°, and 45°

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24
Q

What is an obtuse triangle?

A

A triangle with one angle measuring more than 90°.

Example: A triangle with angles 30°, 60°, and 90°

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25
What is the sum of interior angles in a triangle?
180° Example: If two angles in a triangle are 45° and 60°, the third angle is 75° (180° - 45° - 60° = 75°)
26
What is the exterior angle property of a triangle?
An exterior angle of a triangle equals the sum of the two interior opposite angles. Example: If interior angles are 30° and 70°, the exterior angle at the third vertex is 100°
27
What is the triangle inequality theorem?
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Example: A triangle with sides 3, 4, and 6 is possible because 3+4>6, 3+6>4, and 4+6>3
28
What is a 45°-45°-90° triangle?
A right-angled triangle with two 45° angles. Properties: - If both legs are length x, the hypotenuse is x√2 - Isosceles right-angled triangle Example: If legs are 5 cm, hypotenuse is 5√2 ≈ 7.07 cm
29
What is a 30°-60°-90° triangle?
A right-angled triangle with angles of 30°, 60°, and 90°. Properties: - If shortest side is x, middle side is x√3, longest side is 2x - Half of an equilateral triangle Example: If shortest side is 4 cm, middle side is 4√3 ≈ 6.93 cm, longest side is 8 cm
30
What is a parallelogram?
A quadrilateral with opposite sides parallel. Properties: - Opposite sides equal and parallel - Opposite angles equal - Diagonals bisect each other - Consecutive angles are supplementary
31
What is a rectangle?
A parallelogram with all angles equal to 90°. Properties: - All angles are 90° - Opposite sides equal and parallel - Diagonals equal and bisect each other - Two lines of symmetry
32
What is a rhombus?
A parallelogram with all sides equal. Properties: - All sides equal - Opposite angles equal - Diagonals bisect each other and are perpendicular - Diagonals bisect the angles - Two lines of symmetry (along the diagonals)
33
What is a square?
A rectangle with all sides equal OR a rhombus with all angles equal. Properties: - All sides equal - All angles equal (90°) - Diagonals equal, perpendicular, and bisect each other - Four lines of symmetry
34
What is a trapezium (trapezoid)?
A quadrilateral with exactly one pair of parallel sides. Properties: - One pair of opposite sides are parallel - Can be isosceles (non-parallel sides equal) - Sum of interior angles = 360°
35
What is a kite?
A quadrilateral with two pairs of adjacent sides equal. Properties: - Two pairs of adjacent sides equal - One pair of opposite angles equal - One diagonal bisects the other - One diagonal bisects two angles - One line of symmetry
36
What is the sum of interior angles in any quadrilateral?
360° Example: If three angles in a quadrilateral are 80°, 90°, and 100°, the fourth angle is 90° (360° - 80° - 90° - 100° = 90°)
37
What does congruent mean?
Two shapes are congruent if they have exactly the same size and shape. Symbol: ≅ Example: Two triangles with exactly the same three sides and three angles
38
What is the SSS congruence rule?
Side-Side-Side: Two triangles are congruent if all three sides of one triangle are equal to the corresponding sides of the other triangle.
39
What is the SAS congruence rule?
Side-Angle-Side: Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle.
40
What is the ASA congruence rule?
Angle-Side-Angle: Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding parts of the other triangle.
41
What is the AAS congruence rule?
Angle-Angle-Side: Two triangles are congruent if two angles and a non-included side of one triangle are equal to the corresponding parts of the other triangle.
42
What does similar mean?
Two shapes are similar if they have the same shape but different sizes. Symbol: ∼ Example: A photograph and its enlarged copy
43
How do you know if two triangles are similar?
Two triangles are similar if: - All three corresponding angles are equal, OR - All three pairs of corresponding sides are in the same ratio Example: If all angles in triangle 1 are equal to all angles in triangle 2, the triangles are similar
44
What is a scale factor?
The ratio of corresponding sides in similar shapes. Example: If triangle ABC has sides of 3, 4, and 5 cm, and similar triangle DEF has sides of 6, 8, and 10 cm, the scale factor is 2
45
How do the areas of similar figures relate?
The ratio of areas equals the square of the scale factor. Example: If the scale factor between two similar triangles is 3, the ratio of their areas is 3² = 9
46
What is the center of a circle?
The fixed point from which all points on the circle are the same distance. Symbol: The middle point in ⊙
47
What is the radius of a circle?
A straight line joining the center to any point on the circle. All radii of a circle are equal. Symbol: r Example: The spokes of a wheel
48
What is the diameter of a circle?
A straight line passing through the center and connecting two points on the circle. Formula: d = 2r (diameter = 2 × radius)
49
What is the circumference of a circle?
The distance around the circle (the perimeter). Formula: C = 2πr = πd where r = radius, d = diameter, π ≈ 3.14
50
What is a chord of a circle?
A straight line connecting two points on the circumference. Note: A diameter is a special chord that passes through the center of the circle.
51
What is an arc of a circle?
A portion of the circumference. Example: The curved part between two points on the circumference
52
What is a sector of a circle?
A region bounded by two radii and an arc. Example: A slice of pizza
53
What is a segment of a circle?
A region bounded by a chord and an arc. Example: The region below a chord
54
What happens when a line from the center is perpendicular to a chord?
It bisects (cuts in half) the chord. Example: If a 6 cm chord has a perpendicular line from the center to its midpoint, each half is 3 cm.
55
How do you measure an angle with a protractor?
1. Place the center point of the protractor at the vertex 2. Align the baseline with one arm of the angle 3. Read the measurement where the other arm crosses the scale 4. Make sure to use the correct scale (0-180° vs 180-0°)
56
How do you construct an angle with a protractor?
1. Draw a ray (starting point and extending in one direction) 2. Place the center of the protractor at the starting point 3. Align the baseline with the ray 4. Mark the desired angle measurement 5. Draw a ray from the starting point through the mark
57
How do you construct a perpendicular bisector of a line segment?
1. Set compass width > half the line segment 2. Place compass point at one end, draw arc above and below 3. With same width, place point at other end, draw arcs that intersect the first arcs 4. Draw line through the two intersection points
58
How do you bisect an angle using compass and ruler?
1. With compass point at vertex, draw arc crossing both arms 2. With point at each intersection of arc and arms, draw two arcs that intersect inside the angle 3. Draw line from vertex through intersection point
59
How do you construct a 60° angle using compass and ruler?
1. Draw a ray 2. Set compass to any width 3. Place point at start of ray, draw an arc crossing the ray 4. Without changing width, place point where the arc crossed the ray, draw an arc that intersects the first arc 5. Draw a ray from the start through the intersection point
60
List the equipment needed for the geometry exam
- Sharp pencils - Ruler - Protractor - Compass - Eraser Remember: "No borrowing of equipment during an exam"
61
What should you do first when starting the exam?
1. Read all questions carefully before starting 2. Identify the easy questions to do first 3. Check how many marks each question is worth 4. Plan your time based on mark allocation
62
What should you do if you get stuck on a question?
1. Move on to the next question 2. Circle the question number to remind you to return to it 3. Come back to it after completing other questions 4. If still stuck, try to earn partial marks by showing work
63
How should you approach a construction question?
1. Read instructions carefully 2. Use the correct tools (compass, protractor, ruler) 3. Draw construction lines lightly but visibly 4. DON'T erase construction marks/arcs 5. Label key points clearly 6. Check accuracy when finished
64
How do you earn full marks on a written geometry answer?
1. Use the correct geometric terminology 2. Show ALL your working and calculations 3. Draw clear, labeled diagrams 4. State which properties or theorems you're using 5. Double-check your calculations before finalizing
65
Angles on a straight line
Sum to 180°
66
Angles around a point
Sum to 360°
67
Interior angles of a triangle
Sum to 180°
68
Interior angles of a quadrilateral
Sum to 360°
69
Pythagorean theorem
In a right-angled triangle: a² + b² = c² where c is the hypotenuse (longest side) and a and b are the other two sides
70
Relationship between diameter and radius
d = 2r where d is diameter and r is radius

Geom Gr7 (2 decks)

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