📐 geometry

1. **State the problem:** We have a right-angled triangle with base $21cm$ and area $147cm^2$. We need to find the length of the longest side (the hypotenuse). 2. **Recall the form

1. **Problem 11:** Given $m\angle C = 60^\circ$, $BC = 9$ ft, and $AC = 9$ ft, find missing measures. Since $BC = AC$, triangle $ABC$ is isosceles with $AB$ unknown.

1. **Problem Statement:** We have a square of side length $14$ cm containing a circle centered at $O$ touching all four sides, and two quarter circles drawn from the lower left and

1. **Problem Statement:** We have a figure composed of three semicircles and one circle arranged along the segment $PQ$ where $PQ = 42$ cm and $OP = OQ$. We need to find the total

1. **State the problem:** We are given that $\overleftrightarrow{RT} \parallel \overleftrightarrow{GI}$ and $\overleftrightarrow{UW} \parallel \overleftrightarrow{GI}$. We need to

1. **Problem Statement:** Identify which diagram shows $\triangle UVW$ rotated $30^\circ$ counterclockwise about point $V$. 2. **Understanding Rotation:** A rotation of $30^\circ$

1. **Problem Statement:** Identify which figure among W, X, Y, and Z uses the SAS (Side-Angle-Side) theorem to prove that $\triangle EFG$ is congruent to $\triangle HIJ$. 2. **Reca

1. **Problem Statement:** We are given two triangles $\triangle DEF$ and $\triangle HGF$ with $DE \cong HG$ and $\angle D \cong \angle H$. We need to determine which congruence rul

1. **State the problem:** We are given two triangles $\triangle ABC$ and $\triangle NLM$ with side lengths and angle measures: - $AC = 7$, $m\angle BAC = 80^\circ$, $m\angle ABC =

1. **Problem Statement:** We need to determine which additional congruence mark must be added to the diagram to prove that $\triangle MNO \cong \triangle PQR$ using the ASA (Angle-

1. **Problem Statement:** Determine which statements about congruent triangles are true. 2. **Recall the definition of congruent triangles:** Two triangles are congruent if all thr

1. **State the problem:** We are given two triangles \(\triangle HJK\) and \(\triangle MJL\) with certain congruent sides and angles, and we need to identify which reason correspon

1. The problem describes a coordinate plane with $x$ and $y$ axes intersecting at the origin $(0,0)$. 2. Two points are located on the lower horizontal line near the bottom-left/ce

1. **State the problem:** A bird is initially 4 meters from the base of an oak tree and flies 5 meters to reach the top of the tree. We need to find the height of the tree.

1. **State the problem:** We have three players: Josiah, Ben, and Keith. Ben is 15 feet south of Josiah and 8 feet west of Keith. We want to find the distance Josiah needs to throw

1. **State the problem:** We need to find the measure of $m\angle LPN$ given that $\angle 3$ is a right angle and $\angle MPN \cong \angle RPN$. 2. **Analyze the given information:

1. **Problem Statement:** Identify which pairs of angles are vertical angles. 2. **Definition:** Vertical angles are pairs of opposite angles made by two intersecting lines. They a

1. **State the problem:** Identify which pairs of angles are vertical angles. 2. **Definition:** Vertical angles are pairs of opposite angles made by two intersecting lines. They a

1. **Problem Statement:** We are given two congruent triangles, P and Q, on a coordinate grid with a marked rotation center. We need to find:

1. **State the problem:** We have triangle R with vertices at $ (1,1), (1,4), (3,1) $ rotated about the origin $ (0,0) $ to form triangle S with vertices at $ (1,-1), (1,-3), (4,-1

1. **Problem Statement:** Find the area of a shape that looks like a rectangle with a semicircular indentation on the top side. 2. **Given Dimensions:**