📐 geometry

1. **State the problem:** We have points $X(-2,-2)$ and $X'(-1,0)$, and points $Y(-6,1)$ and $Z(-4,2)$. Points $Y$ and $Z$ are translated by the same vector that moves $X$ to $X'$.

1. **State the problem:** We have two similar triangles DAR and KMR. We know side lengths DA = 16, DR = 11, MR = 14, and we want to find the unknown side length $y = KR$ in triangl

1. **State the problem:** We need to find the length of the minor arc on a circle of radius $r=3$ subtended by an angle of $0.687\pi$ radians. 2. **Formula for arc length:** The le

1. State the problem: Arrange the steps to draw a bearing of 055° from point X in the correct order. 2. Step 1: Draw a vertical line from point X to represent North.

1. **State the problem:** We have a square and a regular hexagon sharing a common side. The perimeter of the square is 24 inches. We need to find the perimeter of the hexagon. 2. *

1. **Problem Statement:** We are given a triangular race track on a Cartesian plane with vertices at $(-2,0)$, $(2,0)$, and $(0,4)$. Each grid square represents an area of 9245 m².

1. Problem 17: Find the total distance an ant travels from point (3,4) to (6,10), then from (6,10) to (10,18) in the Cartesian plane. 2. To find the distance between two points $(x

1. **State the problem:** We need to find the length of the hypotenuse of an isosceles right triangle where each leg measures 12 cm. 2. **Recall the formula:** In an isosceles righ

1. **Problem statement:** We have four collinear points A, B, C, and D arranged such that A - B - C and A - D - B. Given lengths are $AC = 84$ metres, $BC = 5$ metres, and $AD = 61

1. **Problem statement:** Given a circle with center at point $P$, two radii $A$ and $B$ form an angle of $286^\circ$ at $P$. We want to understand the properties of this angle in

1. **State the problem:** We have a diagram with points A, B, C, D, E, F on a gray plane and point G off the plane. We need to answer questions about the plane, coplanar points, no

1. **Problem statement:** Given points A, B, C, D on a circle, with lines AEC and DEB straight, and triangle AED equilateral, prove that triangle ABC is congruent to triangle DCB.

1. The problem is to classify the given quadrilateral based on its properties. 2. The quadrilateral has markings indicating all four sides are congruent (equal in length).

1. **State the problem:** We have two similar teddy bears. The larger bear has height 36 and width 21. The smaller bear has width 7 and height $H$. We need to find $H$. 2. **Recall

1. **State the problem:** We have a square QRPM with sides QR and PM given as expressions in terms of $x$. 2. **Recall properties of a square:** All sides of a square are equal in

1. **Problem statement:** We have an isosceles trapezoid with diagonal length $d$ and the diagonal forms an angle $\alpha$ with the longer base. We want to find the area of this tr

1. **State the problem:** We are given a triangle with angles 68°, 78°, and $x$° and need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interi

1. **State the problem:** We need to find the value of angle $x$ in a triangle where the other two angles are $60^\circ$ and $50^\circ$. 2. **Recall the triangle angle sum rule:**

1. **Stating the problem:** We need to determine which polygons among the given shapes are congruent. 2. **Recall the definition of congruent polygons:** Two polygons are congruent

1. The problem states that quadrilateral ACEG is congruent to quadrilateral MNPR. 2. Congruent quadrilaterals have corresponding sides that are equal in length.

1. **State the problem:** We are given three adjacent angles around a vertex: 56°, 26°, and $n$. We need to find the value of $n$. 2. **Formula used:** The sum of angles around a p