Geometry: Lines, Angles, and Triangles

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Questions and Answers

If two lines intersect, forming four angles, what is the sum of these angles?

$360^\circ$ (correct)
It depends on the angle of intersection
$180^\circ$
$270^\circ$

What distinguishes an acute angle from a right angle?

An acute angle is equal to $90^\circ$, while a right angle is less than $90^\circ$.
An acute angle is less than $90^\circ$, while a right angle is equal to $90^\circ$. (correct)
An acute angle is greater than $90^\circ$, while a right angle is equal to $90^\circ$.
An acute angle is greater than $180^\circ$, while a right angle is less than $90^\circ$.

If two adjacent angles form a right angle ($90^\circ$), what are they called?

Complementary angles (correct)
Supplementary angles
Vertical angles
Reflex angles

What is the relationship between two lines if they intersect at a $90^\circ$ angle?

Perpendicular (C) Signup and view all the answers

If two adjacent angles add up to $180^\circ$, what term describes their relationship?

Supplementary (C) Signup and view all the answers

In Fred's Theorem, if line $l_1$ is parallel to line $l_2$ and both are intersected by transversal $l_3$, what can be said about the 'Big' angles formed?

All 'Big' angles are equal. (A) Signup and view all the answers

According to Fred's Theorem, which angle relationship is correct when two parallel lines are intersected by a transversal?

Vertical angles are equal (C) Signup and view all the answers

In a triangle, what is the sum of all three interior angles?

$180^\circ$ (A) Signup and view all the answers

What is the relationship between the exterior angle of a triangle and its remote interior angles?

The exterior angle is equal to the sum of the remote interior angles. (C) Signup and view all the answers

If all three sides of a triangle are equal, what is this triangle called?

Equilateral (A) Signup and view all the answers

In an equilateral triangle, what is the measure of each interior angle?

$60^\circ$ (C) Signup and view all the answers

If a triangle has two equal sides, what is it called?

Isosceles (D) Signup and view all the answers

In an isosceles triangle, what is the relationship between the angles opposite the two equal sides?

They are equal. (D) Signup and view all the answers

In a scalene triangle, how do the side lengths and opposite angles relate?

The largest angle is opposite the longest side. (D) Signup and view all the answers

What is a 'hypotenuse'?

The side opposite the right angle in a right triangle (B) Signup and view all the answers

What is the relationship between the sides of a 45-45-90 (isosceles right) triangle?

The hypotenuse equals one side times $\sqrt{2}$ (C) Signup and view all the answers

What is the relationship between the sides of a 30-60-90 right triangle?

The side opposite the 60° angle is$\sqrt{3}$ times the side opposite the 30° angle (D) Signup and view all the answers

What is the formula for the area of a right triangle, given the lengths of its two perpendicular sides, $a$ and $b$?

$\frac{1}{2} a \cdot b$ (C) Signup and view all the answers

Under what condition can you apply the Pythagorean theorem?

Right triangle (C) Signup and view all the answers

According to the Pythagorean theorem, what is the relationship between the sides of a right triangle?

$a^2 + b^2 = c^2$ (A) Signup and view all the answers

Which set of side lengths could form a right triangle, according to the Pythagorean Triples?

3 : 4 : 5 (D) Signup and view all the answers

What does it mean for two triangles to be 'congruent'?

They have the same shape and size. (B) Signup and view all the answers

If two triangles have all three angles equal, are they necessarily congruent?

No, they are similar but not necessarily congruent. (B) Signup and view all the answers

What is the minimum information required to prove that two triangles are congruent using the Side-Angle-Side (SAS) postulate?

Two sides and the included angle (B) Signup and view all the answers

Triangle ADE is formed by drawing a line parallel to one side of triangle ABC. What is the relationship between triangles ADE and ABC?

They are similar. (A) Signup and view all the answers

Flashcards

Vertex

The point where the sides of an angle meet.

Leg (of an angle)

The two sides that form an angle.