📐 geometry

1. **State the problem:** Desiree needs to find the total area to cover with stone pavers, which includes the patio and the walkway.

1. **Problem 5: Find the circumference and area of the circle with radius $\sqrt{2}$ cm.** 2. The formulas for circumference and area of a circle are:

1. **Stating the problem:** We have a quadrilateral inscribed in a circle with two known angles 70° and 80°, and two unknown angles labeled $\alpha$ and $\beta$. We need to find th

1. **Énoncé du problème :** Calculer les mesures des angles $\alpha$, $\beta$ et $\gamma$ dans un triangle inscrit dans un cercle de centre $O$, sachant que l'angle central $\angle

1. The problem asks us to determine side lengths that satisfy the triangle inequality theorem. 2. The triangle inequality theorem states that for any triangle with sides $a$, $b$,

1. **State the problem:** We need to find the value of angle $x$ in a triangle where two exterior angles are given: $120^\circ$ at vertex A and $112^\circ$ at vertex C. 2. **Recall

1. **Problem A: Find the measure of each arc of circle ⊙P.** Given: Circle with center P, points A, B, C on circumference. Angle at center P between radii PC and PB is 57°.

1. **State the problem:** We need to find the height of the flagpole, which is the vertical leg of a right triangle. 2. **Identify the known sides:** The horizontal leg is 10 ft, t

1. **State the problem:** We are given a triangle ABC with segment DE inside it, where AB = $11x - 25$ and DE = $4x + 1$. We need to find the length of DE. 2. **Identify the relati

1. **Problem Statement:** We have three lines intersecting at point H: MK, HJ, and HL. Given angles are:

1. **State the problem:** We need to find the distance traveled by a tire after 3 full rotations. The tire has a diameter of 28 inches. 2. **Formula used:** The distance traveled i

1. **Problem statement:** Prove that in an equilateral triangle ABC with points D, E, F on the perpendiculars from an arbitrary point P to the sides, the equality $BD + CE + AF = D

1. **Problem statement:** We have an equilateral triangle ABC and a point P inside it. From P, three perpendiculars are dropped to the sides BC, AC, and AB, meeting at points D, E,

1. **State the problem:** Write a two-column proof for a given geometric statement or theorem. 2. **Understand the two-column proof format:** It consists of two columns: the left c

1. **Problem statement:** Given that BE and AD bisect each other, prove that segment AB is congruent to segment DE. 2. **Understanding the problem:** When two segments bisect each

1. **Problem statement:** We need to find the total length of the highway going around the bay, which consists of two segments: one 7 miles long at a 145° angle and another 2 miles

1. **Stating the problem:** Given points A(3, -2) and B(9, 11), find the direction of translation from point A to point B.

1. **State the problem:** We need to find the volume and surface area of a triangular prism with sides of the triangular base $s_1=3.75$, $s_2=5.5$, $s_3=2.25$, length $L=22$, and

1. **State the problem:** We need to find the volume and surface area of a triangular prism with side lengths of the triangular base $s_1=3.75$, $s_2=5.5$, $s_3=2.25$, length $L=22

1. **Problem statement:** Given $mCG = 6x + 5$, $mAR = 4x + 15$, and $m\angle AEC = 120$, find: a) $x$

1. **State the problem:** Find the area of the L-shaped composite figure made of two rectangles with dimensions 10 cm by 6 cm and 8 cm by 12 cm. 2. **Formula:** Area of a rectangle