Geometry Segment and Angle Relationships Flashcards

Flashcards covering segment addition postulate, midpoints, bisectors, angle relationships, linear pairs, and vertical angles based on the lecture transcript.

What is the core distinction between the Segment Addition Postulate (SAP) and a segment bisector or midpoint?

The Segment Addition Postulate uses the Part + Part = Whole relationship ($AB + BC = AC$), while a midpoint or segment bisector sets Part = Part ($AM = MB$).

If point $E$ is between $G$ and $H$, with $GE = x+2$, $EH = 2x-6$, and $GH = 20$, what is the equation used to find $x$?

$$(x+2) + (2x-6) = 20$$

If point $K$ is between $J$ and $L$, with $JK = 20-x^2$, $KL = 2-x$, and $JL = 10$, what is the calculated value of $JK$ when $x = -4$?

$$JK = 4$$

If point $K$ is between $J$ and $L$, with $JK = 2x+5$, $KL = 5x+3$, and $JL = x^2$, what is the positive value of $x$?

$$x = 8$$

If segment $WT$ bisects $UV$ at point $Y$, with $UY = x-1$ and $UV = x+6$, what is the value of $x$?

$$x = 8$$

If point $Y$ is the midpoint of segment $WT$, with $WY = 3w+5$ and $YT = w+17$, what is the value of $w$?

$$w = 6$$

Using the midpoint formula where endpoint $x_1 = -5$, $y_1 = 4$, midpoint $x_m = -8$, and $y_m = -2$, what is the missing endpoint $(x_2, y_2)$?

$$(-11, -8)$$

If $m\angle RXQ = x+15$, $m\angle QXS = 3x+5$, and $m\angle RXS = 5x-7$, what is $m\angle RXS$?

$$m\angle RXS = 128^\circ$$

If ray $BH$ bisects $\angle ABK$, ray $BC$ bisects $\angle ABH$, $m\angle CBH = x+5$, and $m\angle ABK = 6x-12$, what is $m\angle HBK$?

$$m\angle HBK = 42^\circ$$

If ray $BH$ bisects $\angle ABK$ and ray $BC$ bisects $\angle ABH$, what setup equation relates $m\angle ABH = 2x-40$ and $m\angle ABK = 2x+30$?

$$2(2x-40) = 2x+30$$

Given segment points $B$, $C$, and $D$ with $BD = 7x-10$, $BC = 4x-29$, and $CD = 5x-9$, what setup equation is used?

$$(4x-29) + (5x-9) = 7x-10$$

If two complementary angles are given as $(x+3)^\circ$ and $(2x+3)^\circ$, what equation is used to solve for $x$?

$$(x+3) + (2x+3) = 90$$

If two angles form a linear pair and are given as $(4x+22)^\circ$ and $(8x-10)^\circ$, what equation is used to solve for $x$?

$$(4x+22) + (8x-10) = 180$$

If point $T$ is the midpoint of segment $SU$, with $ST = 12x-5$ and $TU = 4x+19$, what equation is used to solve for $x$?

$$12x-5 = 4x+19$$

If two vertical angles are given as $(4x-14)^\circ$ and $(2x+7)^\circ$, what is the solved value of $x$?

$$x = 10.5$$

What general setup rules apply to geometric equations involving midpoints/bisectors, complementary angles, and supplementary angles?

Midpoint, Bisect, and Vertical angles make equations EQUAL to each other; Complementary and Right angles ADD to $90^\circ$; Supplementary angles and Linear Pairs ADD to $180^\circ$.