📐 geometry

1. **Problem:** Rotate a square centered at the origin with corners at (2, 2), (-2, 2), (-2, -2), and (2, -2) by 90 degrees clockwise around the origin. Find the new coordinates of

1. **State the problem:** Find the value of $x$ that makes triangles $\triangle PQR$ and $\triangle TUV$ similar by using the fact that corresponding angles in similar triangles ar

1. **Problem Statement:** Find the pairs of angles that are Same Side Interior, Same Side Exterior, and Alternate Exterior in the given diagram of two parallel horizontal lines cut

1. **State the problem:** Calculate the perimeter of the first shape with sides 8cm, 8cm, 13cm, 13cm, and 9cm. 2. **Formula:** The perimeter $P$ of a polygon is the sum of the leng

1. **Problem:** Calculate the perimeter of the first shape with sides 8cm, 8cm, 13cm, 13cm, and 9cm. 2. **Formula:** The perimeter $P$ of a polygon is the sum of the lengths of all

1. The problem involves identifying and analyzing pairs of angles formed by intersecting lines and points labeled in a complex geometric figure. 2. Since the problem lists many pai

1. The problem is to calculate the area of a circle given its radius. 2. The formula for the area $A$ of a circle with radius $r$ is:

1. **Nêu bài toán:** Cho tam giác nhọn $ABC$ với $AB < AC$ và đường cao $AH$. $M$, $N$ lần lượt là hình chiếu của $H$ lên $AB$ và $AC$. Chứng minh rằng $$MN = AH \cdot \sin BAC.$$\

1. Tentukan koordinat imej untuk pantulan pada garis tertentu. (a) Pantulan pada garis $y=5$ bagi titik $A(2,8)$.

1. **Problem:** Find the image coordinates after translation. (a) Given point $(-2,4)$ and translation vector $(-3,2)$.

1. **Problem statement:** Given circle $(O)$ with diameter $BC$. Points $A$ and $D$ lie on the semicircle such that arc $BA$ is smaller than arc $BD$. Rays $BA$ and $CD$ intersect

1. **State the problem:** Find the length of a leg $x$ in a right triangle with a $45^\circ$ angle and hypotenuse length 5. 2. **Recall the properties of a $45^\circ-45^\circ-90^\c

1. **Problem statement:** Calculate the perimeter of a right-angled triangle pond where the hypotenuse is 1.46 m and one acute angle is 73°. 2. **Formula and rules:** In a right tr

1. **Problem Statement:** Find the missing values in the first diagram: a) $x$ (cm), b) $b$ (cm), c) $\theta$ (degrees). 2. **Given:** One side is 43.2 cm, an angle is 38°, and sid

1. **Problem statement:** Given square ABCD with \(\angle DAE = 39^\circ\) and \(\angle AGD = 47^\circ\), find \(\angle AFD\). 2. **Known facts:** ABCD is a square, so all sides ar

1. You mentioned you will paste some images with hard angles questions. 2. Please provide the first image or question so I can assist you step-by-step.

1. **Problem Statement:** We have four identical squares arranged in a step pattern on a coordinate grid. Points A and B are given as A(7,4) and B(27,16). We need to find the coord

1. **Problem statement:** Given a geometric figure with points Q, B, S, and H, and lengths QB = 3m and QS = 4m, find the difference in length between SH and BH. 2. **Understanding

1. Bài toán yêu cầu tính diện tích tam giác với độ dài ba cạnh lần lượt là 5m, 8,5m và 10,5m. 2. Công thức sử dụng là công thức Heron để tính diện tích tam giác khi biết độ dài ba

1. **State the problem:** Find the total area of the composite step-shaped polygon with given side lengths. 2. **Analyze the figure:** The polygon can be divided into simpler recta

1. **Problem statement:** We have a rhombus with an area of 32 cm². One diagonal is given as 8 cm, and the other diagonal is labeled as $b$ cm. We need to find the value of $x$ whe