📐 geometry

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

1. The problem is to analyze the triangle with vertices A=(0,0), B=(4,0), and C=(0,4). 2. We start by plotting the points and connecting them to form the triangle.

1. **State the problem:** We have a line segment divided into parts with lengths labeled as $x$, 11, 22, and the entire segment length is 32. 2. **Understand the segments:** The se

1. **State the problem:** Given that the ratios of corresponding sides of triangles DEF and GHI are equal, i.e., $$\frac{DE}{GH} = \frac{DF}{GI} = \frac{EF}{HI}$$, prove that $$\an

1. **State the problem:** Given that \(\frac{DE}{GH} = \frac{DF}{GI} = \frac{EF}{HI}\), prove that \(\triangle DEF \cong \triangle GHI\).

1. **State the problem:** Find the distance between points A(1, -2) and B(7, 4) on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $

1. **State the problem:** Find the distance between points $A(-2, -2)$ and $B(4, 6)$ on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$

1. **State the problem:** Find the midpoint of the line segment joining the points $(-1, -3)$ and $(-3, 14)$. 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoi

1. **State the problem:** Find the midpoint of the line segment joining points A(2, -5) and B(6, 3). 2. **Formula:** The midpoint $M$ of a segment with endpoints $A(x_1, y_1)$ and

1. **State the problem:** We have points $P(a,b)$ and midpoint $M(c,d)$ of segment $PQ$. We want to find expressions for the distances $PM$ and $PQ$. 2. **Recall the distance formu

1. The problem asks to explain the meaning of the expression $PM = \sqrt{(a - c)^2 + (b - d)^2}$ and related formulas. 2. This formula represents the distance between two points $P

1. **State the problem:** We are given point T with coordinates $(0,6)$ and the midpoint $M$ of segment $ST$ as $(3,-4)$. We need to find the coordinates of point $S$.