📐 geometry

1. **State the problem:** Find the distance between the points $(8, -4)$ and $(3, 8)$. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by

1. **State the problem:** Find the distance between the two points $(-4,7)$ and $(7,-5)$ on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1

1. The problem is to find the distance between the two points $(3, -3)$ and $(7, -7)$ on the coordinate plane. 2. We use the distance formula between two points $(x_1, y_1)$ and $(

1. **State the problem:** We are given a triangle with a mid-segment parallel to the base. The top side is labeled $4x$, the mid-segment is labeled 14, one side is labeled $7x - 9$

1. **State the problem:** Find the distance between the two points $(-6, 8)$ and $(9, -4)$ on the Cartesian plane. 2. **Formula used:** The distance $d$ between two points $(x_1, y

1. **State the problem:** Find the distance between the points $A(5,5)$ and $B(8,1)$ on the Cartesian plane. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ an

1. The problem asks to find the distance between two points $(1,1)$ and $(-7,-8)$ on the Cartesian plane. 2. We use the distance formula between two points $(x_1,y_1)$ and $(x_2,y_

1. **Problem Statement:** A plane cuts through a rectangular pyramid passing through three of its lateral faces and is perpendicular to the base. We need to determine the shape of

1. **Problem Statement:** We have a rectangular pyramid and a plane that cuts through the pyramid. The plane passes through the apex (vertex) of the pyramid and is perpendicular to

1. **State the problem:** Find the distance between the two points $(4, 5)$ and $(-3, -2)$ on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1,

1. **State the problem:** We have a composite figure made of a parallelogram stacked on top of a square. The parallelogram has a base of 5 cm and a height of 12 cm. The square has

1. **Problem Statement:** Given a right triangle PQR with right angle at P (\(\angle QPR = 90^\circ\)), \(PQ = 6\) cm, and point M on hypotenuse PR such that \(\angle QPM = \angle

1. **State the problem:** We have triangle $ABC$ with $\angle CAB = 82^\circ$ and $\angle C = 68^\circ$. The perpendicular bisector of side $AB$ intersects $AB$ at $D$ and $BC$ at

1. The problem asks which proportion can be used to find the value of $x$ in similar triangles with sides 6 cm, 2.5 cm, 21 cm, and $x$. 2. For similar triangles, corresponding side

1. **Problem Statement:** We have an isosceles triangle PQR with sides PQ = PR = 5 cm and base QR = 8 cm. A perpendicular from the apex P meets QR at N. We want to find the length

1. **State the problem:** We are given two trapezoids with corresponding sides and need to find the value of $x$ using proportions. 2. **Identify the correct proportion:** The side

1. The problem asks which proportion can be used to find the value of $x$ given the side lengths of two hexagons. 2. The key idea is that corresponding sides of similar figures are

1. The problem is to identify and understand obtuse angles as shown in the graphs labeled 11), 12), and 14). 2. An obtuse angle is defined as an angle greater than 90° and less tha

1. The problem is to classify angles as acute, obtuse, right, or straight based on their descriptions. 2. Definitions:

1. The problem asks to name all angles that have vertex V. 2. An angle is named by three points where the middle point is the vertex. Here, the vertex is V.

1. **Problem Statement:** (a) Calculate angle $\angle ACD$ in quadrilateral $ABCD$ with given sides and angles.