📐 geometry

1. **State the problem:** We need to find the length of a straw placed diagonally inside a rectangular box with dimensions 5 inches by 5 inches by 8 inches. The straw stretches fro

1. **Problem statement:** We have a kite ABCD with diagonals AC and DB intersecting at E such that AC is perpendicular to DB and DE = EB. We are given lengths AE = 8 cm, EC = 10 cm

1. **Problem:** Find the length of segment CD given the expressions for its parts: $2x + 4$ and $4x$. 2. **Formula and rules:** Since CD is divided into two parts, the total length

1. **Problem Statement:** Given two parallel lines $\overrightarrow{IK}$ and $\overrightarrow{LN}$, and a transversal intersecting them at points $J$ and $M$ respectively, with $m

1. **Problem 3: Determine if JK \cong MN** Given:

1. The problem states that \(\triangle 1 \cong \angle 5\) and asks which postulate or theorem justifies that lines \(p\) and \(q\) are parallel. 2. When two lines are cut by a tran

1. **Problem Statement:** Determine which statements can be used to prove that lines $a \parallel b$ and $c \parallel d$ based on angle relationships. 2. **Key Concept:** Lines are

1. The problem gives three angle measures in terms of $x$: $m\angle LJK = 6x$, $m\angle FEB = 7x - 7$, and $m\angle GIA = 4x - 2$. We are asked to find the value of $x$ or the meas

1. **Problem statement:** We have a right cone monument with vertical height $20$ m.

1. **State the problem:** We are given that XZ bisects \(\angle WXY\). The measure of \(\angle WXY\) is \((4x + 2)^\circ\) and the measure of \(\angle WXZ\) is \((3x - 8)^\circ\).

1. **State the problem:** Given that $m\angle ADC = 180^\circ$ and $m\angle ADB = 152^\circ$, find $m\angle BDC$ in degrees. 2. **Understand the setup:** Since $m\angle ADC = 180^\

1. **Problem Statement:** We have a parallelogram PQRS with sides PQ = 13 units, QR = (2x - 1) units, and RS = (2x - 3) units. We need to find the measure of side PS. 2. **Importan

1. The problem states that the dashed line is perpendicular to line segment AB and passes through point E. 2. If AE \cong BE, it means point E is the midpoint of segment AB.

1. The problem asks to find the image of rectangle ABCD after two transformations: a reflection across the y-axis followed by a dilation with a scale factor of $\frac{1}{2}$. 2. Th

1. The problem states that we have two triangles, \(\triangle ABC\) and \(\triangle EDC\), with given congruent angles \(\angle B \cong \angle E\) and \(\angle BCA \cong \angle EDC

1. **State the problem:** We need to find the measure of the smallest angle in a triangular pond where the interior angles are given as $(2y - 4)^\circ$, $(y + 7)^\circ$, and $(3y

1. **Problem Statement:** Given triangle PSR with point S on base QR, and PS \cong QS, angles \angle P = 48^\circ and \angle S = 84^\circ. We need to determine which comparisons am

1. **State the problem:** We have a triangle with angles measuring 72°, 53°, and 5n°. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of a triangle is alw

1. The problem is to find the angle of an isosceles triangle given some information. 2. An isosceles triangle has two equal sides and two equal angles opposite those sides.

1. **Problem statement:** Given a circle with center O and points A, B, C, D on the circumference, where OA is parallel to CD, and angles $\angle OAB = 23^\circ$ and $\angle OCB =

1. **Problem:** Plot the circle with center coordinates (5,4) and radius 2 units. 2. **Formula:** The equation of a circle with center $(h,k)$ and radius $r$ is given by: