📐 geometry

1. **Problem statement:** Triangle C is rotated 180° clockwise about the origin. We need to find the new location of Triangle C after this rotation. 2. **Rotation formula:** For a

1. **State the problem:** We have two similar triangles, $\triangle ABC \sim \triangle ADE$, and we need to find the length $u = AE$. 2. **Recall the property of similar triangles:

1. **State the problem:** We are given a triangle with an internal point E on side BC. We know one angle is $46^\circ$ at vertex C and another angle $y^\circ$ at vertex B between s

1. **Problem statement:** Given parallelogram KLMN with side KL labeled as $x$, side LM as 16, and other segments marked with equal lengths, find the value of $x$. 2. **Recall prop

1. **State the problem:** We have triangle $\triangle STU$ with side $s = 250$ inches opposite angle $S$, angle $\angle U = 17^\circ$, and angle $\angle S = 52^\circ$. We need to f

1. **State the problem:** We have triangle UVW with side $w=35$ inches opposite angle $W=154^\circ$, and angle $U=10^\circ$. We need to find the length of side $u$ opposite angle $

1. **Problem Statement:** We have two right triangles with sides labeled as follows: the first triangle has sides $x$, $y$, and $6$ with a height of $2$ corresponding to side $6$.

1. **Problem Statement:** We are given two right triangles with smaller right triangles inside them. We need to find relationships between the sides using the Pythagorean theorem.

1. **State the problem:** Given that $AB \cong DE$, $\angle C \cong \angle F$, and $\angle B \cong \angle E$, prove that $\triangle ABC \cong \triangle DEF$. 2. **Recall the Angle-

1. **Problem statement:** Find the volume of each pyramid given the dimensions. 2. **Formula:** The volume $V$ of a pyramid is given by

1. Problem 10: Calculate the total weight in ounces of ten cone-shaped ice cubes with radius 1.5 inches and height 2 inches, given 1 cubic inch ≈ 0.55 ounce. 2. Use the volume form

1. **Stating the problem:** We are given that triangles ABC and EHK are congruent ($\triangle ABC \equiv \triangle EHK$), and segments MBHP and NCHL are drawn such that $BC \cong B

1. **Problem statement:** Find the area of the shaded region in a large circle with center $Q$ and area $9\pi$ square inches, where three equal semicircles are drawn on the diamete

1. The problem asks to find the circumference of a circle given the diameter $d = 9$ inches. 2. The formula for the circumference $C$ of a circle is:

1. **Problem statement:** Given triangle ABC with AC = AB and angles DCA and ACB supplementary, find (a) \(\angle ACB\), (b) \(\angle ABC\), and (c) \(\angle CAB\). 2. **Key facts

1. Énonçons le problème : Nous avons un triangle avec un angle de 25° et des côtés de 17,6 et 35 unités. Nous devons trouver la mesure de l'angle $v$ au sommet. 2. Utilisons la loi

1. **State the problem:** We need to find the measure of angle $\angle V$ in triangle $VWX$ where the sides are $VW=5$, $VX=7$, and $XW=6$. 2. **Formula used:** To find an angle wh

1. **State the problem:** We need to find the measure of angle $\angle X$ in triangle $WYX$ where the sides are $WY=12$, $XY=13$, and $WX=15$. 2. **Formula used:** To find an angle

1. **State the problem:** We need to find the measure of angle $\angle G$ in triangle $FGH$ where the sides are given as $FH=15$, $HG=10$, and $FG=13$. 2. **Formula used:** To find

1. **State the problem:** We need to find the measure of angle $Y$ in triangle $XYZ$ where the sides are $XY=12$, $XZ=15$, and $YZ=20$. 2. **Formula used:** Use the Law of Cosines

1. **State the problem:** We need to find the measure of angle $Y$ in triangle $XYZ$ where the sides opposite to vertices $X$, $Y$, and $Z$ are 13, 7, and 12 respectively. 2. **Rec