Final Geometry Revision Ch 7, 8, 9

Flashcards covering key geometry concepts including triangle congruence, parallel line theorems, perpendicular bisectors, and triangle inequalities based on the Level J revision worksheet.

In Ch 7.1 Q6, if $O$ is the midpoint of $AB$ and $CD$, which segments are congruent as a direct result of the definition of a midpoint?

$CO = DO$ and $AO = BO$

According to the Exterior Angle Theorem used in Ch 7.2 Q7, how does the measure of exterior angle $\angle EDA$ compare to the interior angle $\angle DCA$ of $\triangle ADC$?

$$m\angle EDA > m\angle DCA$$

In Ch 8.1 Q11, if $MN \perp AB$, what is true about $\angle AMN$ and $\angle BMN$?

$\angle AMN$ and $\angle BMN$ are right angles

In an equilateral triangle where $M$ is the midpoint of base $BC$, what is the geometric relationship between the median $AM$ and the base $BC$?

$$AM \perp BC$$

What is the conclusion of the Theorem used in Ch 8.2 Q18 regarding points $A$ and $M$ being equidistant from the endpoints of segment $BC$?

$AM$ is the perpendicular bisector of $BC$

In the diagram for Ch 8.3 Q24, what is the relationship between $\angle 3$ and $\angle 5$?

$\angle 3$ and $\angle 5$ are alternate interior angles

In Ch 8.4 Q25, if $m\angle RAC = 45^\circ$ and $m\angle ACM = 45^\circ$, and they are alternate interior angles, what property proves $AR \parallel CM$?

The Alternate Interior Angles Converse

According to Ch 8.4 Q31, if line $t \perp m$ and line $m \parallel n$, what must be the relationship between line $t$ and line $n$?

$$t \perp n$$

In Ch 8.5 Q34, if $l \parallel m$ and $n \parallel k$, what is the relationship between $\angle 5$ and $\angle 2$?

$$\angle 5 \cong \angle 2$$

In Ch 8.5 Q36, if lines are parallel, what is the sum of the measures of interior angles on the same side ($\angle 1$ and $\angle 2$)?

$m\angle 1 + m\angle 2 = 180^\circ$ (they are supplementary)

In Ch 9.1 Q45, what is the theorem regarding the relationship between the two acute angles of a right triangle?

The acute angles of a right triangle are complementary

In Ch 9.4 Q70, if side $AC > AB$ in $\triangle ABC$, what is the corresponding inequality for the angles opposite those sides?

$$m\angle ABC > m\angle ACB$$

What is the Triangle Inequality Theorem as stated in Ch 9.4 Q70?

$$AB + BC > AC$$

In Ch 9.4 Q71, given a triangle with side lengths $MN = 8.5$ and $NP = 6.2$, what is the range of possible values for the third side $MP = y$?

$$2.3 < y < 14.7$$

In Ch 9.3 Q64, if $\angle KJI$ and $\angle LIJ$ are right angles, $JL = KI$ (hypotenuses), and $JI = JI$ (common leg), which theorem proves $\triangle KJI \cong \triangle LIJ$?

The Hypotenuse-Leg (HL) theorem