📐 geometry

1. **Problem Statement:** Given a right triangle ABC with right angle at A, side AB = 4, side AC = 3, and BC is the hypotenuse. Find the measure of the shaded angle (assumed to be

1. **Problem statement:** We have a right triangle with hypotenuse 24 and base 9, and a vertical side labeled $x$. We need to find the length of $x$. 2. **Formula used:** In a righ

1. **State the problem:** We need to find the area of a rectangle with side lengths $5\sqrt{7}$ cm and $2\sqrt{7}$ cm. 2. **Formula for the area of a rectangle:**

1. **Problem statement:** Reflect the point $(4,6)$ across the y-axis and x-axis. 2. **Reflection across the y-axis:**

1. **State the problem:** We have points $X(-5,7)$, $Y(-4,-11)$, and $Z(9,-6)$. They are reflected over the x-axis to points $X'$, $Y'$, and $Z'$.

1. The problem is to find or understand 2 line segments. 2. A line segment is a part of a line bounded by two distinct endpoints.

1. **State the problem:** We need to find the area of the irregular polygon drawn on the grid where each square represents 1 cm by 1 cm. 2. **Calculate the area:** Count the full 1

1. **State the problem:** Ruby has 4 identical right-angled triangles with sides 12 cm, 16 cm, and 20 cm. She arranges them to form a star. We need to find the perimeter of the sta

1. **State the problem:** We have triangle $\triangle ABC$ with sides $a = 15$ cm, $b = 18$ cm, and angle $\angle C = 48^\circ$. We want to find side $AB$ and angle $A$ using both

1. **State the problem:** We have a quadrilateral with four angles: 70°, 76°, 90°, and an unknown angle $r$. We need to find the value of $r$. 2. **Recall the formula:** The sum of

1. **State the problem:** We are given the exterior angles of a convex hexagon as expressions involving $t$: $5t - 38^\circ$, $7t - 43^\circ$, $36^\circ$, $t + 20^\circ$, $6t - 24^

1. **State the problem:** We need to find the number to multiply each distance on the map (in cm) to get the actual distance (in km). 2. **Identify the scale:** The scale given is

1. **State the problem:** We need to find the scale factor to convert map distances to actual distances, and then use it to find the actual distance from Osc's campsite to the gene

1. **State the problem:** We need to find the number of sides $n$ of a regular polygon given that each interior angle measures 172°. 2. **Formula for interior angle of a regular po

1. **State the problem:** We have a scale drawing of a motel where 6 inches on the drawing corresponds to 30 yards in actual length. The east side of the motel measures 2 inches on

1. **State the problem:** We have a convex polygon with six interior angles given as: - 131°

1. **Problem:** Name the geometric solid formed when a right triangle is rotated around the x-axis. The solid formed is a **cone** because rotating a right triangle around one of i

1. **State the problem:** Chani starts with point $S(-8,6)$ and applies two transformations: a translation right 5 units, then a 180° rotation around the origin.

1. **State the problem:** Duncan is transforming point $S(1,0)$ by translating it down 3 units, then reflecting over the x-axis. We need to check if Duncan's work is correct. 2. **

1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite the 60° angle (the hypotenuse) is 5 inches, and we need to find the length of si

1. The problem asks for the coordinate notation representing a translation left 5 units followed by a 180 degree rotation around the origin. 2. Translation left 5 units means subtr