📐 geometry

1. **State the problem:** We need to find the values of angles $x$, $y$, and $z$ in the quadrilateral $ABCD$ where $\angle B = 121^\circ$, $\angle A = 40^\circ$, and $AB \parallel

1. **State the problem:** Find the area of the curved segment of a circle given the radius of curvature $R=100$ m and sagitta (height) $h=100$ m. 2. **Given data:**

1. **State the problem:** We need to find the area of the curved region (a segment of a circle) given the radius of curvature and the sagitta (height) of the arc. 2. **Given data:*

1. **Stating the problem:** We have two parallel lines \(m\) and \(a\) cut by two transversals \(r\) and \(v\). Given angles are \(5a\) near \(r\) and \(m\), \(85^\circ\) near \(r\

1. **Stating the problem:** We are given seven angles labeled $m\angle 1$ through $m\angle 7$ with specific degree measures. The problem involves understanding how these angle meas

1. **State the problem:** We have a parallelogram with an area of 40 units squared, a height of 5 units, and an unknown base $b$. We need to find the value of $b$. 2. **Formula for

1. **State the problem:** We have a right triangle with base length 4 units and height $x$ units. The area of the triangle is given as 16 units². We need to find the missing length

1. **State the problem:** Given two triangles $DEF$ and $GHI$ with right angles at $E$ and $H$ respectively, and the proportion $\frac{DE}{GH} = \frac{EF}{HI}$ along with $xE \cong

1. **State the problem:** Prove that $$\frac{EF}{HI} = \frac{DF}{GI}$$ given the proportions $$\frac{DE}{EF} = \frac{EF}{GH}$$ and $$\frac{GH}{HI} = \frac{HI}{DF}$$, and that $$\an

1. **State the problem:** Given that $\frac{JL}{NL} = \frac{KL}{ML}$ and $JL = ML$, prove that $\angle J \cong \angle N$. 2. **Analyze the given information:** We have two triangle

1. **State the problem:** Given triangles DEF and HGI with DE = EF, GH = HI, and \(\angle E \cong \angle H\), prove that EF = DF and HI = GI.

1. **State the problem:** Prove that $\angle E \cong \angle H$ given the similarity of triangles $\triangle DEF \sim \triangle GHI$ and the ratio $\frac{DE}{GH} = \frac{DF}{GI} = E

1. **Problem 4: Which graph shows a line with an undefined slope?** A line with an undefined slope is a vertical line because the change in $x$ is zero, making the slope formula $m

1. **Write the inverse of the conditional:** "If Deanna eats the last cookie, then Leon will buy more." The inverse negates both the hypothesis and conclusion:

1. **Problem:** Write the inverse of the conditional: "If Deanna eats the last cookie, then Leon will buy more." 2. **Inverse** means negating both hypothesis and conclusion:

1. **Problem:** Name two lines or segments that lie in plane ADH. The plane ADH contains points A, D, and H. Lines or segments lying in this plane must connect these points.

1. **State the problem:** We are given that segment QN bisects angle PQS, meaning it divides angle PQS into two equal angles. 2. **Given:**

1. **State the problem:** We are given the coordinates of the vertices of a quadrilateral representing a town's park: $(-9,0)$, $(-8,4)$, $(0,2)$, and $(-1,-2)$. We need to find th

1. **Problem statement:** We need to find values of $x$ and $y$ such that the two right triangles in item 6 are congruent by the HL (Hypotenuse-Leg) theorem. 2. **HL theorem:** Two

1. **State the problem:** We want to find values of $x$ and $y$ such that two right triangles are congruent by the HL (Hypotenuse-Leg) theorem. 2. **Recall the HL theorem:** Two ri

1. **State the problem:** Calculate the surface area of a gas tank composed of a cylinder with two hemispheres on each end. 2. **Given data:** Diameter of cylinder and hemispheres