Given $riangle ABC$ and $riangle DEF$. If $AB = DE$, $\angle B = \angle E$, and $BC = EF$, which congruence postulate proves that $\triangle ABC \cong \triangle DEF$?

Which of the following statements is always true for a parallelogram?

A triangular garden has a base of $12 meters and a height of \8$ meters. What is the area of the garden?

In a circle, an inscribed angle subtends an arc of $80^{\circ}$. What is the measure of the inscribed angle?

In a right-angled triangle, if the side opposite to angle $\theta$ is $6 units and the hypotenuse is \10$units, what is the value of$\sin\theta$?

Which of the following quadrilaterals has diagonals that are always perpendicular bisectors of each other?

The volume of a cylinder is given by the formula:

Which of the following is NOT a valid congruence criterion for triangles?

If a line is tangent to a circle, then the radius drawn to the point of tangency is always _________ to the tangent line.

In a $30^{\circ}-60^{\circ}-90^{\circ}$right triangle, if the shortest leg has a length of$x$, what is the length of the hypotenuse?

Triangle $ABC$ is congruent to triangle $DEF$. If $AB = 2x+1$, $DE = 11$, $BC = y-2$, and $EF = 5$, find the values of $x$ and $y$.

Calculate the volume of a square pyramid with a base side length of $8 cm and a height of \7.5$ cm.

In parallelogram $ABCD$, $\angle A = (2x - 15)^{\circ}$ and $\angle C = (x + 50)^{\circ}$. Also, $\angle B = (y)^{\circ}$. Find the values of $x$ and $y$.

A circular arc measures $90^{\circ} and has a radius of \40$cm. Calculate the length of the arc. Use$\pi \approx 3.14159$. Round your answer to two decimal places.

A ladder is leaning against a wall. The top of the ladder reaches a height of $20 meters. If the angle of elevation of the ladder with the ground is \65^{\circ}$, what is the length of the ladder to two decimal places?

A composite shape consists of a rectangle with a length of $10 units and a width of \10 units, and a triangle attached to one of its sides. The triangle has a base of \10 units (same as the rectangle's side) and a height of \9.6$ units. Calculate the total area of the composite shape.

Given quadrilateral $ABCD$ with $AD = CB$ and $AB = CD$. Prove that $ABCD$ is a parallelogram.

Given that lines $AE$ and $BD$ intersect at point $C$. If $C$ is the midpoint of $AE$ and $BD$, prove that $\triangle ABC \cong \triangle DEC$.

Given a circle with center $O$ and a chord $AB$. If $OM \perp AB$, where $M$ is a point on $AB$, prove that $M$ is the midpoint of $AB$. (i.e., the perpendicular from the center to a chord bisects the chord).