Lines, Angles, and Triangles flashcards

0/60

60 cards remaining

Take the chapter practice test

All 60 cards in this deckShow

Algebraic angle expressionsAngle Relationships and Parallel Lines: Name the angle rule before solving for the variable.
When should I use vertical and supplementary angles?Angle Relationships and Parallel Lines: Use opposite and straight-line angle relationships.
What method supports algebraic angle expressions?Angle Relationships and Parallel Lines: 3x+10 and 2x+20 supplementary ⇒ 5x+30=180
Parallel lines and a transversalAngle Relationships and Parallel Lines: Parallel lines let matching angle positions carry the same measure.
Vertical and supplementary anglesAngle Relationships and Parallel Lines: Opposite angles match; angles on a straight line add to 180°.
What must I check in angle relationships and parallel lines?Angle Relationships and Parallel Lines: Use parallel-line angle theorems only when parallelism is stated or established
What method supports parallel lines and a transversal?Angle Relationships and Parallel Lines: same-side interior angles sum to 180°
What method supports vertical and supplementary angles?Angle Relationships and Parallel Lines: vertical angles equal; linear-pair sum=180°
When should I use algebraic angle expressions?Angle Relationships and Parallel Lines: Solve an equation from an angle relationship.
When should I use parallel lines and a transversal?Angle Relationships and Parallel Lines: Transfer angle measures using corresponding or alternate angles.
Isosceles angle constraintsTriangle Angles and Exterior Angles: The two equal base angles split what the vertex angle leaves.
When should I use triangle angle sum?Triangle Angles and Exterior Angles: Recover a missing interior angle.
What method supports isosceles angle constraints?Triangle Angles and Exterior Angles: base angle=(180°−vertex angle)/2
Exterior-angle theoremTriangle Angles and Exterior Angles: An outside angle equals the two inside angles away from it.
Triangle angle sumTriangle Angles and Exterior Angles: The three inside angles share 180°.
What must I check in triangle angles and exterior angles?Triangle Angles and Exterior Angles: The exterior angle uses the two remote interior angles, not the adjacent interior angle
What method supports exterior-angle theorem?Triangle Angles and Exterior Angles: exterior angle=remote angle₁+remote angle₂
What method supports triangle angle sum?Triangle Angles and Exterior Angles: A+B+C=180°
When should I use isosceles angle constraints?Triangle Angles and Exterior Angles: Use equality of base angles in an algebraic model.
When should I use exterior-angle theorem?Triangle Angles and Exterior Angles: Find an exterior angle from two remote interior angles.
Algebra in corresponding sidesCongruent Triangles and Corresponding Parts: Congruence gives the equation, but the target may be a length rather than x.
When should I use corresponding parts?Congruent Triangles and Corresponding Parts: Use the ordered triangle names to match vertices and sides.
What method supports algebra in corresponding sides?Congruent Triangles and Corresponding Parts: corresponding side expressions are equal
Sufficiency of congruence informationCongruent Triangles and Corresponding Parts: A congruence claim must fix both shape and size.
Corresponding partsCongruent Triangles and Corresponding Parts: Match the first letters, then the second, then the third.
What must I check in congruent triangles and corresponding parts?Congruent Triangles and Corresponding Parts: Congruence requires sufficient information: SSS, SAS with included angle, ASA/AAS, or right-triangle HL; AAA proves only similarity and SSA is not generally sufficient
What method supports sufficiency of congruence information?Congruent Triangles and Corresponding Parts: SSS, SAS, ASA, AAS, or right-triangle HL
What method supports corresponding parts?Congruent Triangles and Corresponding Parts: △ABC≅△DEF ⇒ AB=DE, BC=EF, AC=DF
When should I use algebra in corresponding sides?Congruent Triangles and Corresponding Parts: Use a congruence equality to find a length.
When should I use sufficiency of congruence information?Congruent Triangles and Corresponding Parts: Distinguish sufficient congruence criteria from angle-only similarity.
Nested triangles and parallel segmentsSimilar Triangles and Proportional Sides: Parallel cuts make a same-shape smaller triangle.
When should I use similarity scale?Similar Triangles and Proportional Sides: Use one pair of corresponding sides to find another.
What method supports nested triangles and parallel segments?Similar Triangles and Proportional Sides: If DE∥BC with D on AB and E on AC, AD/AB=AE/AC
Similarity sufficiencySimilar Triangles and Proportional Sides: Two angle matches fix triangle shape.
Similarity scaleSimilar Triangles and Proportional Sides: Same shape means every matching side scales by one multiplier.
What must I check in similar triangles and proportional sides?Similar Triangles and Proportional Sides: AA, proportional SSS, or proportional SAS with included angle can establish similarity; corresponding side ratios must use one consistent direction
What method supports similarity sufficiency?Similar Triangles and Proportional Sides: AA ⇒ similar; proportional sides ⇒ SSS similarity
What method supports similarity scale?Similar Triangles and Proportional Sides: A′B′/AB=A′C′/AC=k
When should I use nested triangles and parallel segments?Similar Triangles and Proportional Sides: Use parallelism to establish similarity before a proportion.
When should I use similarity sufficiency?Similar Triangles and Proportional Sides: Use two matching angles to establish similarity without size equality.
Coordinate distanceThe Pythagorean Theorem and Coordinate Distance: The coordinate changes form the legs of a right triangle.
When should I use find a hypotenuse?The Pythagorean Theorem and Coordinate Distance: Apply the Pythagorean theorem to perpendicular legs.
What method supports coordinate distance?The Pythagorean Theorem and Coordinate Distance: d=√[(x₂−x₁)²+(y₂−y₁)²]
Find a missing legThe Pythagorean Theorem and Coordinate Distance: Subtract squares when the longest side is known.
Find a hypotenuseThe Pythagorean Theorem and Coordinate Distance: Square the legs, add, and take the root.
What must I check in the pythagorean theorem and coordinate distance?The Pythagorean Theorem and Coordinate Distance: The hypotenuse is opposite the right angle; the Pythagorean equation does not apply to an arbitrary nonright triangle
What method supports find a missing leg?The Pythagorean Theorem and Coordinate Distance: b=√(c²−a²)
What method supports find a hypotenuse?The Pythagorean Theorem and Coordinate Distance: c=√(a²+b²)
When should I use coordinate distance?The Pythagorean Theorem and Coordinate Distance: Use horizontal and vertical coordinate differences as right-triangle legs.
When should I use find a missing leg?The Pythagorean Theorem and Coordinate Distance: Subtract a known leg square from the hypotenuse square.
Recover an area from special sidesSpecial Right Triangles: Use the ratio to find the legs, then multiply and halve.
When should I use 45-45-90 triangles?Special Right Triangles: Use equal legs and a √2 hypotenuse multiplier.
What method supports recover an area from special sides?Special Right Triangles: 30-60-90 area=(s²√3)/2
30-60-90 trianglesSpecial Right Triangles: Short leg, long leg, hypotenuse follow 1, √3, 2.
45-45-90 trianglesSpecial Right Triangles: Equal right-triangle legs give a diagonal √2 times as long.
What must I check in special right triangles?Special Right Triangles: Identify which side is opposite 30° or 60°; ratios do not depend on drawing orientation
What method supports 30-60-90 triangles?Special Right Triangles: s:s√3:2s
What method supports 45-45-90 triangles?Special Right Triangles: leg:leg:hypotenuse=1:1:√2
When should I use recover an area from special sides?Special Right Triangles: Combine a special-triangle ratio with the area formula.
When should I use 30-60-90 triangles?Special Right Triangles: Relate the short leg, long leg, and hypotenuse.