Quick Review Flashcards - Click to flip and test your knowledge!
Question
What is the definition of a triangle?
Answer
A plane figure bounded by three straight line segments.
Question
In a triangle with sides of different lengths, which angle is the largest?
Answer
The angle opposite the side with the greatest measure.
Question
If the angles of a triangle have different measures, which side is the shortest?
Answer
The side opposite the angle with the smallest measure.
Question
What is true about the angles opposite the equal sides of an isosceles triangle?
Answer
The angles opposite the equal sides are also equal.
Question
If two angles of a triangle are equal, what can be concluded about the sides opposite them?
Answer
The sides opposite the equal angles are equal in length.
Question
What is the relationship between the angles of an equilateral triangle?
Answer
All three angles are equal in measure.
Question
The line segment joining the mid-point of a side to the opposite vertex is called a _____.
Answer
Median
Question
How many medians can be drawn in a single triangle?
Answer
Three
Question
What is the term for the single point where all three medians of a triangle intersect?
Answer
Centroid
Question
In what ratio does the centroid divide each median of a triangle?
Answer
The centroid divides each median in the ratio $2:1$.
Question
Term: Altitude of a triangle
Answer
Definition: The length of the perpendicular drawn from a vertex to the opposite side.
Question
The point of intersection of the three altitudes of a triangle is called the _____.
Answer
Orthocentre
Question
What is the sum of the interior angles of any triangle?
Answer
The sum is equal to two right angles, or $180^{\circ}$.
Question
According to the Exterior Angle Theorem, what is the measure of an exterior angle formed by producing one side of a triangle?
Answer
It is equal to the sum of the two interior opposite angles.
Question
How does the measure of an exterior angle compare to either of its interior opposite angles?
Answer
The exterior angle is always greater than each of the interior opposite angles.
Question
What is the maximum number of right angles a triangle can contain?
Answer
One
Question
What is the maximum number of obtuse angles possible in a single triangle?
Answer
One
Question
In a right-angled triangle, what is the sum of the two acute angles?
Answer
The sum of the two acute angles is $90^{\circ}$.
Question
What is the minimum number of acute angles every triangle must have?
Answer
Two
Question
If two triangles have two pairs of angles equal to each other, what is the relationship between their third angles?
Answer
The third angles of both triangles are also equal.
Question
When are two triangles considered to be 'congruent'?
Answer
When they have exactly the same shape and the same size.
Question
In the context of congruency, what does it mean for triangles to have the 'same shape'?
Answer
The angles of one triangle are equal to the corresponding angles of the other triangle.
Question
In the context of congruency, what does it mean for triangles to have the 'same size'?
Answer
The sides of one triangle are equal to the corresponding sides of the other triangle.
Question
What mathematical symbol is used to denote that two triangles are congruent?
Answer
The symbol $\cong$.
Question
What does the abbreviation 'C.P.C.T.C.' stand for?
Answer
Corresponding Parts of Congruent Triangles are Congruent.
Question
Where do corresponding angles lie in relation to equal sides in congruent triangles?
Answer
Corresponding angles lie opposite to the equal sides.
Question
State the SAS (Side-Angle-Side) condition for triangle congruency.
Answer
Two triangles are congruent if two sides and the included angle of one are equal to two sides and the included angle of the other.
Question
In the SAS congruency axiom, where must the equal angle be positioned relative to the equal sides?
Answer
The equal angle must be the included angle between the two equal sides.
Question
A quadrilateral whose diagonals bisect each other at right angles is a _____.
Answer
Rhombus
Question
State the ASA (Angle-Side-Angle) condition for triangle congruency.
Answer
Two triangles are congruent if two angles and the included side of one are equal to two angles and the included side of the other.
Question
State the AAS (Angle-Angle-Side) condition for triangle congruency.
Answer
Two triangles are congruent if two angles and one side of one triangle are equal to the corresponding angles and side of the other triangle.
Question
When using the AAS axiom, what is the required position of the equal sides relative to the equal angles?
Answer
The equal sides must be corresponding sides, meaning they are opposite to equal angles in both triangles.
Question
How can the AAS axiom be derived from the ASA axiom?
Answer
By using the angle sum property to prove that if two angles are equal, the third angle (and thus the included side's relationship) is also equal.
Question
State the SSS (Side-Side-Side) condition for triangle congruency.
Answer
Two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle.
Question
State the RHS (Right angle-Hypotenuse-Side) condition for triangle congruency.
Answer
Two right-angled triangles are congruent if the hypotenuse and one side of one are equal to the hypotenuse and one side of the other.
Question
Why is the order of vertices critical when writing a congruency statement like $\Delta ABC \cong \Delta DEF$?
Answer
The order must ensure that corresponding vertices, angles, and sides occupy the same positions in the notation.
Question
If $\Delta ABC \cong \Delta EFD$, which vertex in the second triangle corresponds to vertex $A$?
Answer
Vertex $E$.
Question
If $\Delta ABC \cong \Delta FED$, which side in the first triangle corresponds to side $ED$?
Answer
Side $BC$.
Question
What is the geometric relationship between the adjacent angles of a parallelogram?
Answer
The adjacent angles are supplementary, meaning they sum to $180^{\circ}$.
Question
In a square, what is the measure of each interior angle?
Answer
$90^{\circ}$
Question
If a point $P$ is equidistant from the arms of $\angle ABC$, what does the ray $BP$ do to that angle?
Answer
Ray $BP$ bisects $\angle ABC$.
Question
In an isosceles triangle, what is the relationship between the altitude to the base and the base itself?
Answer
The altitude bisects the base.
Question
If the perpendicular bisector of a chord $AB$ passes through the centre $O$ of a circle, what is the relationship between the segments $AP$ and $PB$?
Answer
The segments $AP$ and $PB$ are equal ($AP = BP$).
Question
What is the sum of angles around a single point on a plane?
Answer
$360^{\circ}$
Question
In a parallelogram, what is the relationship between opposite sides?
Answer
Opposite sides are equal in length and parallel.
Question
If two triangles are congruent by the SSS rule, what can be concluded about their corresponding angles?
Answer
All corresponding angles are equal by C.P.C.T.C.
Question
Concept: Concurrent lines
Answer
Definition: Lines that all intersect at a single common point.
Question
What is the relationship between the hypotenuse and the other sides in a right-angled triangle?
Answer
The hypotenuse is the longest side of the triangle.
Question
If $\Delta ABC$ is an equilateral triangle and $AD$ is an altitude, what is the measure of $\angle BAD$?
Answer
$30^{\circ}$
Question
Which congruency condition requires a right angle, the longest side, and one other side to match?
Answer
The RHS (Right angle-Hypotenuse-Side) condition.
Question
Can two triangles be proven congruent using only their three angles (AAA)?
Answer
No, AAA only proves the triangles have the same shape (similarity), not the same size.
Question
In the ASA condition, if the side provided is NOT the one between the two angles, which condition should be used instead?
Answer
The AAS (Angle-Angle-Side) condition.
Question
If a triangle has angles of $40^{\circ}$, $60^{\circ}$, and $80^{\circ}$, which side is the longest?
Answer
The side opposite the $80^{\circ}$ angle.
Question
What is the value of each angle in an equilateral triangle?
Answer
$60^{\circ}$
Question
If a triangle is right-angled and isosceles, what are the measures of its acute angles?
Answer
Both acute angles are $45^{\circ}$.