Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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if two lines in the same plane do not intersect, the lines must be para…
1. Correct 2. Incorrect 3. Correct
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classify each statement in the table as correct or incorrect. select on…
# Explicación paso a paso: ## Paso 1: Recordar la definición de líneas paralelas Dos líneas en el mismo plano que no se intersectan son paralelas. Pero si las líneas no están en e…
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given: ad ≅ cb, ∠dac ≅ ∠bca. prove: △adc ≅ △cba. look at the proof. nam…
B. SAS Postulate
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9. what additional information do you need to prove $\triangle abccong\…
\(\overline{AC}\cong\overline{EC}\)
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8 look at the figures. how can you prove these triangles are congruent?…
B. $\triangle ABC\cong\triangle DEF$ by the SAS Postulate.
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∠abc≅∠def ∠cab≅∠fde ∠bca≅∠efd
B. $\angle CAB\cong\angle FDE$
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given: ab ≅ ed, ad ≅ eb prove: △abd ≅ △edb ab ≅ ed given ad ≅ eb given …
A. SSS Postulate
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quiz: triangle congruence by sss 1. what additional information do you …
\(\overline{AC}\cong\overline{DF}\)
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4. look at the figure. how can you prove △abd and △acd are congruent? i…
$\triangle ABD\cong\triangle ACD$ by the SAS Postulate.
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how do you construct congruent segments, segment bisectors, angles, and…
To construct congruent segments, use a compass to copy a length. For segment bisectors, use a compass to create arcs from both endpoints and connect the intersection points of the…
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given: $overline{ad}congoverline{cb},angle adbcongangle cbd$ prove: $\t…
B. SAS Postulate
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how do you know that each of these constructions is valid when it is ma…
These constructions are valid when they follow the rules and principles of Euclidean geometry such as congruence postulates, circle properties, and straight - line axioms.
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what additional information do you need to prove △abc ≅ △def by sas? △a…
$\angle ABC\cong\angle DEF$
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1 look at the figures. how can you prove the triangles are congruent? △…
$\triangle ABC\cong\triangle DEF$ by the SSS Postulate.
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which angles are consecutive interior angles? ∠ihk and ∠jkh ∠ihk and ∠i…
$\angle IHK$ and $\angle JKH$
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which angles are corresponding angles? ∠mli and ∠kln ∠hil and ∠hig ∠kln…
$\angle KLN$ and $\angle HIG$
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ce and fh are parallel lines. which angles are supplementary angles? ∠e…
∠EDB and ∠EDG
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which of the following represents the interval (0, ∞) on a number line?…
A line extending to the right from 0 with an open circle at 0
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pr and su are parallel lines. which angles are adjacent angles? ∠pqt an…
∠PQT and ∠PQO
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qs and tv are parallel lines. which angles are corresponding angles? ∠s…
$\angle SRU$ and $\angle VUW$
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bd and eg are parallel lines. which angles are corresponding angles? ∠e…
$\angle EFC$ and $\angle BCA$
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km and np are parallel lines. which angles are supplementary angles? ∠p…
$\angle POQ$ and $\angle POL$
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which angles are adjacent angles? ∠vux and ∠tus ∠vux and ∠yxz ∠vux and …
$\angle VUX$ and $\angle YXZ$, $\angle VUX$ and $\angle WXU$
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which angles are adjacent angles? ∠hik and ∠gfi ∠hik and ∠efi ∠hik and …
$\angle HIK$ and $\angle JIK$
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jl and mo are parallel lines. which angles are vertical angles? ∠mnk an…
$\angle MNK$ and $\angle ONP$
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6. for the following general equations of circles, complete the square …
a. Standard form: $(x + 7)^{2}+(y + 6)^{2}=49$, Center: $(-7,-6)$, Radius: $7$ b. Standard form: $(x - 16)^{2}+(y - 7)^{2}=9$, Center: $(16,7)$, Radius: $3$
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su and vx are parallel lines. which angles are adjacent angles? ∠str an…
$\angle STR$ and $\angle UTW$
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if $overleftrightarrow{ik}$ and $overleftrightarrow{ln}$ are parallel l…
$58^{\circ}$
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look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarr…
$66$
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if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel l…
$122$
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17. look at the figure. if △imc≅△klj, then ∠m is ○ ∠j ○ ∠b. ○ ∠l ○ ∠k.
$\angle J$
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look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarr…
$140$
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1. look at the figure. if △imc ≅ △jbk, then ____ = jb. ○ (overline{mc})…
$\overline{MC}$
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look at this diagram: if $overleftrightarrow{np}$ and $overleftrightarr…
$52$
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look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarr…
$120^{\circ}$
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5. find the distance between the two points, (-6,4) and (-1,8). state t…
Simplest radical form: $\sqrt{41}$ Decimal form: $6.40$
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find the coordinates of the vertices of each figure after the given tra…
$E'(- 2,2),J'(-1,-2),R'(-3,-3),S'(-5,-2)$
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find the length of the third side. if necessary, write in simplest radi…
$4$
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find the length of the third side. if necessary, write in simplest radi…
$8$
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find the length of the third side. if necessary, write in simplest radi…
$3$
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find the length of the third side. if necessary, write in simplest radi…
$\sqrt{33}$
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13. write an algebraic formula for a rotation in which the preimage coo…
The algebraic formula for the rotation is \((x,y)\to(-x,-y)\) ### 14.
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13 write an algebraic formula for a rotation in which the preimage coor…
### 13 # Explanation: ## Step1: Analyze pre - image and image points Pre - image points are \(A(1,-3)\), \(B(1,1)\), \(C(5,1)\) and image points are \(A'(-1,3)\), \(B'(-1,-1)\), \…
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los siguientes triángulos son congruentes y sus partes correspondientes…
# Explicación: ## Paso 1: Identificar ángulos congruentes Los ángulos correspondientes en triángulos congruentes son iguales. Si $\triangle ABC\cong\triangle XYZ$, entonces $\angl…
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hallar el valor de x.
# Explicación: ## Paso 1: Aplicar la propiedad de ángulo exterior El ángulo exterior de un triángulo es igual a la suma de los dos ángulos interiores no adyacentes. Entonces, $140…
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4. what are all the x - intercepts? (-2.55,0), (2.55,0) (0, 36) (-3,0),…
# Explicación paso a paso: ## Paso 1: Definición de intersección con el eje x Las intersecciones con el eje x son los puntos donde la curva cruza el eje x, es decir, donde $y = 0$…
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1) rotation 180° about the origin 3) rotation 90° counterclockwise abou…
For 180 - degree rotation about the origin, use the rule $(x,y)\to(-x,-y)$ for each vertex of the polygon. For 90 - degree counter - clockwise rotation about the origin, use the r…
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if △sqr is similar to △spt, what is the length of st? 13 in 5.2 in 4.8 …
2 in
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10. the figure below shows similar triangles abc and ade. based on the …
10 cm
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9. the sides of two equilateral triangles are in the ratio 3:5. if a si…
40 inches
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complete the proof that ∠yxz≅∠sut. statement reason 1 (overleftrightarr…
Transitive property of congruence
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which is an x - intercept of the graphed function? (-1, 0) (0, 4) (0, -…
A. (-1, 0)
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analyzing graphs which lists all of the x - intercepts of the graphed f…
(1, 0), (2, 0), and (-3, 0)
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complete the proof that ∠txu ≅ ∠tux. statement reason 1 $overleftrighta…
Transitive Property of Congruence
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which point is inside of the parallelogram? a. (7,5) b. (5,6) c. (6,8) …
B. (5,6)
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clasificar cada figura como una recta, semirrecta o segmento de recta. …
# Explicación: ## Paso 1: Definir segmento de recta Un segmento de recta está formado por dos puntos y el tramo de recta que los une. Las figuras (a), (b) y (c) tienen dos puntos …
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which point is outside of the parallelogram? a. (5,5) b. (5,4) c. (4,5)…
D. (5, 6)
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solve for y.
$5\sqrt{2}$
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how many lines of symmetry does the picture have? a. 2 b. 1 c. 0 d. 3
C. 0
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trazar un ángulo de 85° utilizando la regla y el transportador.
# Explicación: ## Paso 1: Coloca la base del transportador en la línea Asegúrate de que la línea coincida con la base del transportador. ## Paso 2: Encuentra el 85° en el transpor…
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en la siguiente figura, n se encuentra entre m y p. hallar la ubicación…
La ubicación de $N$ divide el segmento $MP$ en una razón de $4$ a $1$, es decir, $N$ está a $\frac{4}{5}$ de la distancia desde $M$ hasta $P$.
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en el △abc, ab || de. dado que ca = 30, cd = 21 y ab = 40, hallar de. d…
# Explicación: ## Paso 1: Aplicar teorema de triángulos semejantes Como $\overline{AB}\parallel\overline{DE}$, entonces $\triangle CDE\sim\triangle CAB$. Entonces, $\frac{CD}{CA}=…
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hallar el volumen de un cilindro oblicuo con una base de 6.5 cm de radi…
# Explicación: ## Paso 1: Escribir la fórmula del volumen del cilindro El volumen $V$ de un cilindro se calcula con la fórmula $V=\pi r^{2}h$, donde $r$ es el radio de la base y $…
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unit 1 post test year long (total 61 pts) 1. (4 pts) the length of a re…
Length = 47 Width = 26
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your name 1. days of the week and months choose and circle the correct …
1. Days of the Week and Months: Requires knowledge of Italian day and month names. 2. Greetings: - Walk into an office at 7 pm: Buonasera (Good evening). - Someone shakes your han…
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alexis created a new tessellation using the same squares. what transfor…
Translation
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part a based on the diagram above and the given information, what is th…
Part A: 72° Part B: alternate exterior angles are congruent
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solve quickly. a sheet of paper 19 cm by 8 cm is rolled into a cylinder…
i) Diameter $\approx6.05$ cm ii) Area of the base $\approx28.75$ $cm^{2}$ iii) Curved - surface area = 152 $cm^{2}$ iv) Volume $\approx229.94$ $cm^{3}$
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parallel lines $overleftrightarrow{ef}$ and $overleftrightarrow{ab}$ ar…
$x = 2$
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given $overleftrightarrow{bh}paralleloverleftrightarrow{rp}$, $angle hx…
The reason for step 5 is the Converse of the Alternate Interior Angles Theorem.
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problem 5 this diagram shows three lines with some missing angle measur…
The missing angles (clock - wise starting from the top - left intersection near the $70^{\circ}$ angle): $110^{\circ},70^{\circ},110^{\circ}$; at the other intersection (clock - w…
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problem 9: spiral review determine the missing angle measure in the equ…
60°
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problem 8: spiral review determine the missing angle measure in the iso…
30°, 30°
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problem 7: spiral review determine the missing angle measure in the rig…
$65^{\circ}$
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question 15 a student claims the following \if two angles are supplemen…
B. A pair of vertical angles C. A pair non - vertical angles formed by two intersecting lines D. Two right angles that share a common vertex but do not share a common side E. A pa…
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lines f, g and h are shown below with angles 1, 2, 3, 4, 5, 6, 7 and 8.…
B. converse of the corresponding angles postulate
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problem 1 here are three intersecting lines. determine the missing angl…
The three missing angles are $45^{\circ}$, $100^{\circ}$, $55^{\circ}$ (in the order as we analyze them based on the given $45^{\circ}$ and $80^{\circ}$ angles in the problem, fro…
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two angles are supplementary if the sum of their angle measures is equa…
$x = 9$ $m\angle ABC = 38^{\circ}$ $m\angle CBD = 52^{\circ}$ No, the shared ray does not bisect the angle.
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turn and talk: reflex angles are defined in terms of a given angle; the…
1. The measure of the reflex angle of an angle \(x^{\circ}\) is \((360 - x)^{\circ}\). 2. When bisecting a 46° angle, each of the two newly - formed adjacent angles has a measure …
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task 2: use the protractor to find the measure of each of the following…
| Angle | Measurement | Classification | | ---- | ---- | ---- | | $\angle ABD$ | [To be measured with protractor] | [To be classified based on measurement] | | $\angle EBF$ | [To …
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a ray is a part of a line that starts at an endpoint and extends foreve…
A. (Draw two rays with a common endpoint for the first part and two non - intersecting rays for the second part). B. (Draw adjacent angles $\angle ABC$ and $\angle CBD$. Names for…
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are the pockets on this shirt congruent? if so, describe a composition …
A. The pockets on this shirt are congruent. To map the pocket on the left to the pocket on the right, reflect it across the row of buttons.
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the composition of transformations $r_{y = - 5}circ r_{(90^{circ},a)}$ …
The perimeter of △ABC is equal to the perimeter of △XYZ. The perimeter of △ABC is 26. A possible set of values of AB, BC, and AC is 8, 9, 9.
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find a congruence transformation that maps △vyw to △xnf. which congruen…
C. $R_{y - axis}(\triangle VYW)$
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name read the problem. answer the questions to help understand the prob…
1. Area is the amount of space inside a two - dimensional shape. 2. Yes. 3. Each small square represents 1 square unit. 4. The shaded part of the rectangle. 5. Count the number of…
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find the volume of the figure. show or explain your thinking. 1.10 answ…
The volume of the figure is equal to the number of small cubes in the figure (in cubic - units, assuming each small cube has a volume of 1 cubic - unit). Since the figure is not c…
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find the midpoint m of the line segment joining the points c = (8, - 7)…
$(1,-1)$
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find the midpoint m of the line segment joining the points p = (-4, -7)…
$(-2,-4)$
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find the midpoint m of the line segment joining the points c = (-3, 7) …
$M=(-1,5)$
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in the figure below, b is between a and c, and c is between b and d. if…
7
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in the figure below, o is between m and p, and n is the midpoint of $ov…
12
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in the figure below, f is between e and g, and g is between f and h. if…
$14$
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in the figure below, s is between q and t, and r is the mid - point of …
$6$
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in the figure below, b is between a and c, and c is between b and d. if…
9
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13 draw, lm that bisects ∠tlc. if ∠tlc = 8x + 26 and ∠clm = 3x + 15, fi…
$x = 2$ $m\angle TLC=42$ $m\angle TLM = 21$
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review 1.1 - 1.4 geometry use the diagram to answer the following quest…
1. $\overrightarrow{KR}$ 2. 4; $\overrightarrow{RM}$, $\overrightarrow{RK}$, $\overrightarrow{RS}$, $\overrightarrow{RT}$; $\overrightarrow{RS}$ and $\overrightarrow{RT}$ 3. $\ove…
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(from unit 1, lesson 3.) 8. a, b, and c are the centers of the 3 circle…
B. \(HA\), D. \(CD\), E. \(BD\)
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7. this diagram is a straightedge and compass construction. a is the ce…
a. $\overline{AB}$ and $\overline{CD}$ b. $\overline{AC}$ and $\overline{AD}$ (or $\overline{BC}$ and $\overline{BD}$, or $\overline{AM}$ and $\overline{BM}$)
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(from unit 1, lesson 4.) 6. in the construction, a is the center of one…
Segments \(AC\), \(AD\), \(BC\), \(BD\)
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5. this diagram is a straightedge and compass construction. which trian…
The triangle formed by the intersection points of the circles (assuming circles have equal radii in the straightedge and compass construction) is equilateral because all of its si…