📐 geometry

1. **State the problem:** Find the coordinates of the point that lies $\frac{3}{10}$ of the way from point $A(-5, -8)$ to point $B(12, 6)$.\n\n2. **Formula used:** The coordinates

1. **Stating the problem:** Given that \(\angle 3 = 74^\circ\), find the measures of other related angles formed by two parallel lines \(l\) and \(m\) cut by two transversals. 2. *

1. The problem asks to identify the angle pair relationship between angles 6 and 7 formed by two parallel lines $l$ and $m$ intersected by a transversal. 2. Important rules for ang

1. The problem asks to complete the statement: "Parallel lines always have the same ____________." The options are y-intercept, x-intercept, and gradient. 2. In geometry, parallel

1. The problem asks: What is the reason for 6? CPCTC? 2. CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a theorem used in geometry to justify th

1. **State the problem:** We need to complete the proof that $\triangle VYZ \cong \triangle WXZ$ given that $\triangle VWZ$ and $\triangle XYZ$ are equilateral triangles. 2. **Reca

1. The problem asks us to identify which two triangles are congruent by the SSS (Side-Side-Side) Theorem and to complete the congruence statement. 2. The SSS Theorem states that if

1. The problem asks to identify the correct way to name the tiling pattern based on the given vertex configurations. 2. In tiling notation, numbers represent the number of sides of

1. **State the problem:** Find the area of a circle with radius 7 inches using $\pi = 3.14$ and do not round the answer. 2. **Formula:** The area $A$ of a circle is given by the fo

1. **State the problem:** We need to find the area of a training field formed by a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Identify given

1. **Problem statement:** We have a right triangle RQS with a right angle at S. The hypotenuse RQ is 4 units long, and the angle at Q is 49°. 2. **Goal:** Find the length of side R

1. **State the problem:** We need to find the length of side $HI$ in a right triangle $IJH$ where the right angle is at $J$, side $IJ = \sqrt{22}$, and angle $I = 61^\circ$. 2. **I

1. **Problem Statement:** Find the surface area of the rectangular prism with a triangular base where the base triangle has sides 4 ft, 3 ft, and 5 ft (right triangle), and the pri

1. **Problem Statement:** Calculate the area of a rectangular room. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. The problem asks to identify the correct sequence of transformations that correspond to the coordinate transformation $$(x, y) \to (y, -x + 3)$$ for triangle ABC. 2. First, cons

1. **Problem Statement:** Determine which statements about the sequence of transformations from the preimage triangle ABC to the image triangle A''B''C'' are true, given the coordi

1. **State the problem:** We have five figures: Cylinder #1 (height 5 in, radius 6 in), Cone #1 (height 5 in, radius 6 in), Cylinder #2 (height 15 in, radius 6 in), Cone #2 (height

1. **Problem Statement:** Find the volume of a sphere with diameter 72 cm. 2. **Formula:** The volume $V$ of a sphere is given by

1. **Problem statement:** In a circle with center O, the measure of the minor arc PYQ is 110 degrees. We need to find the measure of the major arc PYQ. 2. **Formula and rules:** Th

1. **State the problem:** We need to find the image of triangle $\triangle KLM$ after reflecting it over the vertical line $x = -5$. 2. **Recall the reflection rule:** When reflect

1. **State the problem:** We need to find the image of rectangle JKLM after reflecting it over the line $y=2$. 2. **Reflection formula:** When reflecting a point $(x,y)$ over the h