📐 geometry

1. The problem is to find the angle given the final answer is 40°. 2. Since the final answer is already provided as 40°, no further calculations are needed.

1. **Problem statement:** We have a parallelogram PQRS and a rhombus RSTU with S on OT. Given \(\angle QPS = 66^\circ\) and \(\angle RTU = 37^\circ\), find \(\angle PSO\). 2. **Key

1. **Problem statement:** We are given a figure with parallelogram PQRS and rhombus RSTU sharing side RS. Point S lies on OT. Given angles are \(\angle QPS = 66^\circ\) and \(\angl

1. **State the problem:** We have a square-based pyramid with a slant edge of 13 cm and a base length of 10 cm. We need to find the slant height of the pyramid. 2. **Understand the

1. Let's start by stating the problem: We need to understand the basics of circles in math. 2. The general equation of a circle with center at $(h,k)$ and radius $r$ is given by:

1. **State the problem:** We have two circles: one centered at point A with radius equal to the length of segment AB, and another centered at point C with the same radius AB. These

1. **Problem Statement:** Prove that each diagonal of a rectangle divides it into two congruent triangles. 2. **Recall the properties of a rectangle:**

1. **State the problem:** Find the area of a polygon with right angles and given side lengths: bottom 13 in, two vertical sides 6 in each, two vertical segments 4 in each at the to

1. **State the problem:** Find the area of a polygon with sides meeting at right angles and given side lengths. 2. **Approach:** Since the polygon is rectilinear (all angles are ri

1. **State the problem:** Find the area of an irregular polygon composed of three rectangular segments with right angles. 2. **Analyze the figure:** The base length is 13 inches, h

1. **State the problem:** Find the area of a parallelogram with base $14$ yd and height $14$ yd. 2. **Formula:** The area $A$ of a parallelogram is given by:

1. The problem states that triangles $\triangle ABC$ and $\triangle CBE$ are congruent, i.e., $\triangle ABC \cong \triangle CBE$. 2. This means all corresponding sides and angles

1. The problem states that quadrilateral $ABCD$ has one pair of opposite sides $AB$ and $CD$ that are both congruent and parallel. 2. Alessandra wants to prove that $ABCD$ is a par

1. The problem is to select the correct rephrased statement that Vera can use to prove that any rectangle is also a parallelogram. 2. Recall the definitions:

1. The problem states that quadrilateral $ABCD$ has diagonals $AC$ and $BD$ that bisect each other at point $E$. 2. We want to prove that $\overline{AB} \parallel \overline{CD}$ by

1. The problem asks to select the correct rephrased statement for Kun's proof that if opposite sides of a quadrilateral are congruent, then it is a parallelogram. 2. The key proper

1. **Problem statement:** Alva wants to prove that opposite sides in a parallelogram are congruent by establishing the congruence of a single pair of triangles. 2. **Given:** Quadr

1. The problem is to prove that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. 2. Recall the definitions:

1. **Stating the problem:** We have a quadrilateral $ABCD$ with $AB \parallel CD$ and $\angle ADC = 90^\circ$. We need to determine which two statements among A, B, C, and D must b

1. The problem involves plotting points and understanding their positions on a coordinate plane. 2. We have two points: Kidnapper at $(1,3)$ and Victim at $(8,10)$.

1. **State the problem:** We need to calculate the volume of a cuboid with given dimensions: height = 4 cm, length = 19 cm, and a diagonal of one face = 21 cm. 2. **Recall the form