📐 geometry

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

1. **State the problem:** We have a triangle with sides labeled $r$, 17, and 5, and an angle of $32^\circ$ opposite side $r$. We need to find the length of side $r$. 2. **Identify

1. **Problem statement:** We are given a triangle PQR with sides $PQ=15$, $PR=9$, and the included angle $\angle P=136^\circ$. We need to find the length $p$ of the side opposite a

1. **Problem statement:** Reflect the given shapes in the specified lines.

1. The problem asks which statement must be true about triangles that are similar. 2. By definition, similar triangles have the same shape but not necessarily the same size.

1. The problem states that triangle ABC is similar to triangle FGH, and we need to find the proportion to calculate the length of segment BC in centimeters. 2. Similar triangles ha

1. **Problem Statement:** We are given two similar quadrilaterals PQRS and TUVW. We need to determine which statement about their angles or side ratios must be true based on simila