📐 geometry

1. **Problem:** Determine the measure of angle $\angle L$ in the right triangle with vertices $F, L, H$, where $\angle F$ is the right angle, $FL = 2.5$ cm, $FH = 3.7$ cm, and $\an

1. ปัญหา: พิจารณาสมการกราฟ 4 สมการ และตรวจสอบว่าแต่ละสมการเป็นกราฟประเภทใด (วงกลม, พาราโบลา, วงรี, ไฮเพอโรบลา) 2. กฎพื้นฐานสำหรับสมการกราฟกราฟโคเนีย (conic sections):

1. **Problem Statement:** Tara is building a fence represented by Rectangle ABCD with vertices A(6,8), B(6,1), C(10,1), D(10,8). Each unit on the graph equals 12 yards. Tara dilate

1. **State the problem:** Keisha used a photo measuring 4 inches by 6 inches and made a copy measuring 8 inches by 12 inches. We need to find the scale factor of the dilation. 2. *

1. The problem involves calculating the area or perimeter of various circle sectors and a triangle based on given radii and dimensions. 2. The formulas for circle sectors are:

1. **State the problem:** We have a rectangle with side lengths 5 and 10 units. It is dilated by a scale factor of 5. We need to find the perimeter and area of the original rectang

1. **State the problem:** We need to find the value of $d$ given two adjacent angles formed by intersecting lines: one angle is $94^\circ$ and the other is $(8d+6)^\circ$. 2. **Use

1. The problem asks to draw a triangle with vertex A at the origin, vertex B on the negative x-axis, and vertex C in the third quadrant. 2. Let's define the coordinates:

1. **State the problem:** Given a triangle with an angle of 40° and two sides adjacent to angle A measuring 21 and 27, find the angle A and the length of side $x$ opposite the 40°

1. **Problem Statement:** Find the measure of angle 7 given the expressions for two angles formed by intersecting lines: $3x + 90$ and $2x + 155$. 2. **Understanding the problem:**

1. The problem is to find the area of a shape. 2. To find the area, we need to know the type of shape and its dimensions.

1. **State the problem:** Calculate the area of the right triangle inscribed in the circle with base 8 ft and height 15 ft.

1. **State the problem:** We have a right triangle with base $30$ units and height $12$ units, and a circle inside it with radius $8$ units. We need to find:

1. **Stating the problem:** We have a regular hexagon with side length $16$ and an inscribed right triangle sharing one side of the hexagon as its base. The triangle's height is $1

1. **State the problem:** Find the distance between the points $(-10.6, -17.8)$ and $(15.4, 8.1)$. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2,

1. **State the problem:** Find the distance between the points $ (16, -8) $ and $ (-11, -20) $ on the coordinate plane. 2. **Formula used:** The distance $ d $ between two points $

1. **State the problem:** Given two parallel lines $p$ and $q$ cut by a transversal, we are to understand the relationships between angles $\angle 1$, $\angle 2$, and $\angle 3$. 2

1. **Problem Statement:** Given two parallel lines $p$ and $q$ cut by a transversal $w$, with $m\angle 1 = 55^\circ$, find the measures of $\angle 2$ and $\angle 3$ and explain the

1. **State the problem:** We have a regular polygon with 12 sides (a dodecagon). One interior angle is given as $23x - 11$ degrees. 2. **Find the sum of the interior angles:** The

1. **Problem statement:** We have a right triangle with points G, H, and F, where GH is parallel to DE. Given that GH is 7 more than EH, FH = 6, and DE = 15, we need to find the le

1. **Stating the problem:** Determine whether the given pairs of triangles are similar or not, and if similar, identify the similarity criteria. 2. **Similarity criteria for triang