📐 geometry

1. **State the problem:** We have triangle ABC with vertices A(-3, -2), B(0, 4), and C(4, 1).

1. **State the problem:** We have a right triangle with legs 8 and 32, and hypotenuse $x$. We need to find the value of $x$. 2. **Formula used:** In a right triangle, the Pythagore

1. **State the problem:** Identify all segments parallel to XT in the given 3D figure (a cube-like rectangular prism). 2. **Recall the rule:** Segments are parallel if they lie in

1. **Problem statement:** Given the segment lengths $XL = x + 7$ and $LV = 2x - 5$, find the length of $XY$. 2. **Understanding the problem:** Points $X$, $L$, and $V$ lie on the s

1. **State the problem:** We have an isosceles trapezoid EFGH with sides EG and FH given by expressions $EG = 2s + 93$ and $FH = s + 98$. We need to find the value of $s$. 2. **Rec

1. **State the problem:** We have an isosceles trapezoid GHIJ with $m\angle H = 6z + 28^\circ$ and $m\angle I = 130^\circ$. We need to find the value of $z$. 2. **Recall properties

1. **State the problem:** We are given a trapezoid RTUW with midsegment \( \overline{SV} \). The lengths are given as \( RW = -2p + 65 \), \( SV = p + 50 \), and \( TU = p + 71 \).

1. **State the problem:** We have an isosceles trapezoid DEFG with sides DF and EG given by expressions $DF = 10s + 1$ and $EG = 7s + 40$. We need to find the value of $s$. 2. **Re

1. **State the problem:** We have an isosceles trapezoid EFGH with $m\angle F = c + 49^\circ$ and an adjacent angle measuring $133^\circ$. We need to find the value of $c$. 2. **Re

1. **State the problem:** We are given a trapezoid STVW with midsegment RU. The lengths are given as VW = $3y - 56$, RU = $-2y + 64$, and ST = $y$. We need to find the value of $y$

1. **State the problem:** We are given a trapezoid QRTU with midsegment PS. The lengths are:

1. The problem states that the diameter of a circle is 16 meters, and we need to find the area of the circle rounded to the nearest hundredth. 2. Recall the formula for the area of

1. **State the problem:** We have two intersecting lines forming four angles. One angle is 64°, another angle y is 90°, and we need to find the measure of angle x. 2. **Recall impo

1. The problem asks to find the measure of the missing angle $a$. 2. We know that the two angles $a$ and 51° form a right angle, which means their sum is 90°.

1. **Problem Statement:** (i) Show that any two angle bisectors of a triangle meet in a point.

1. **Problem Statement:** We are given an affine plane with axioms I1 to I4 and need to prove four properties about parallel lines, points on lines, total points, and provide an ex

1. **Problem Statement:** Given two chords AB and CD of a circle intersecting at point E inside the circle, prove that $|AE| \cdot |EB| = |CE| \cdot |ED|$.

1. **Problem statement:** In pentagon ABCDE, all sides are equal and angles A, B, C are equal. We need to prove all five angles are equal, making it a regular pentagon. 2. **Given:

1. **Problem Statement:** Solve the two triangles given the following data: - Triangle 1: \(\angle A = 19^\circ\), \(a = 30\) yd, \(b = 12\) yd, \(m\angle B = 69.5^\circ\), \(m\ang

1. **State the problem:** We are given a triangle with some sides and angles labeled inconsistently. We need to solve the triangle, meaning find all unknown sides and angles.

1. **Problem statement:** In pentagon ABCDE, all sides are equal and angles A, B, C are equal. We need to prove all five angles are equal, making it a regular pentagon. 2. **Given: