This document contains 26 math word problems related to geometry and calculating lengths and distances between points on a number line. The problems involve finding unknown segment lengths given relationships between various points such as one segment being twice as long as another or one point being the midpoint between two other points. Multiple choice answers are provided for each problem.
The power point explains the concept of quadrilateral.It also helps us to understand important theorem " the sum of all the angles in a quadrilateral is 180 degrees".
The power point explains the concept of quadrilateral.It also helps us to understand important theorem " the sum of all the angles in a quadrilateral is 180 degrees".
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Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject, tricks of tackling the questions and above all enthusing students with self confidence, ambition and a 'never say give up' spirit. As secrets of success these are no substitutes for hard work and patience.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
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Instructions for Submissions thorugh G- Classroom.pptx
Geometría
1. UNIVERSIDAD NACIONAL AGRARIA DE LA SELVA
Centro Preuniversitario. Mayo - Agosto 2021
Semana 1 – Segmentos
Curso: Geometría Docente: José O. Castillo Cornelio
Tingo María 2021
1. En una línea recta se ubican los puntos
consecutivos A, B y C, tal que 2(AC) =
3(AB) y BC = 7. Calcule AC.
a) 1 2 b) 15 c) 18 d) 21 e) 16
2. Si AD = 36, calcula “a”.
a) 5 b) 12 c) 4 d) 9 e) 10
3. Se tienen los puntos colineales y consecu-
tivos A, B, C y D; tales que: AD = 18, BD =
13 y AC = 12. Calcula “BC”.
a) 3 b) 4 c) 5 d) 6 e) 7
4. Sobre una recta se ubican los puntos
consecutivos A, B, C y D. Calcular “CD”,
si: AD = 20 y se cumple:
5
CD
3
BC
2
AB
=
=
a) 12 b) 9 c) 6 d) 10 e) 8
5. En una línea recta se ubican los puntos
consecutivos A, B y C, tal que 2(AC) =
3(AB) y BC = 7. Calcule AC.
a) 12 b) 15 c) 18 d) 21 e) 16
6. Dado los puntos colineales y consecutivos
A, B, C, D y E, donde AC = BD y AD + BE
= 21. Hallar BD si C es punto medio de
AE.
a) 7 b) 8 c) 9 d) 12 e) 14
7. Sobre una recta se toman los puntos
consecutivos A, E, B, P y C; E es punto
medio de AB y P es punto medio de EC.
Calcular PC si 𝐴𝐵 + 2(𝐵𝐶) = 42.
a) 10 b) 12.5 c) 10.5 d) 14 e) 21
8. Sobre una recta se ubican los puntos
consecutivos A, B, C, D y E, tal que:
AC = CE, AB + CD = 18 y DE – BC = 4.
Calcule CD.
a) 6 b) 7 c) 8 d) 10 e) 14
9. Sean los puntos colineales y consecutivos
A, B, C, D y E, tal que AB + CD = 3(BC) y
DE = AB. Si luego se ubica el punto medio
M de BE, donde MD = 4 y AE = 17. Cal-
cular CM.
a) 2 b) 3 c) 3.5 d) 4 e) 4.5
10. Dados los puntos colineales y consecuti-
vos A, B, C, D y E tales que, B es punto
medio de AC, C es punto medio de AD y D
punto medio de CE. Hallar la medida del
segmento que resulta al unir los puntos
medios de BC y DE si AE = 42.
a) 21 b) 24 c) 24.5 d) 26 e) 28
11. Dado los puntos colineales y consecutivos
A, B, C, D y E, donde AC=BD y
AD+BE=21. Hallar BD si C es punto medio
de AE
.a) 7 b) 8 c) 9 d) 12 e) 14
12. Se marca los puntos colineales de una
recta: A, B, C, D, E, tales que:
DE
BC
BD
AC
3
1
, =
= y
36
2
3
=
+ DE
AB . Hallar AE.
a) 44 b) 54 c) 48 d) 68 e) 34
13. Se marcan los puntos colineales y conse-
cutivos A, B, M, C, siendo M punto medio
de BC. Hallar:
2
2
2
2
BM
AM
AC
AB
+
+
.
a) 1 b) 2 c) 8 d) 4 e) 3
a - b a + b
A C
B
a
D
2. Tingo María 2020
14. Sobre una recta se ubican los puntos
colineales A, B, C y D de tal manera que
16
;
12 =
=
+ BD
BC
AB y
24
=
AD . Hallar BC.
a) 1 b) 10 c) 8 d) 4 e) 7
15. Sobre una línea recta se consideran los
puntos consecutivos A, B, C, D y cumple la
siguiente relación:
m
CD
BD
AB 4
.
2
.
4 =
−
− . Si
m
AB 3
= y m
AC 5
= . Hallar la lon-
gitud del segmento AD.
a) 2m b) 15m c) 3m d) 7m e) 10
16. Sobre una línea recta se consideran los
puntos consecutivos A, B, C, D. Si
m
CD
m
AB 1
;
3 =
= . Hallar la longitud
del segmento que tiene por extremos los
puntos medios de AC y BD.
a) 2m b) 3m c) 5m d) 9m e) 11m
17. Se tienen los puntos colineales A, B, y C;
se toman los puntos medios M y N de AC y
AB respectivamente. Hallar BC. Si: MN=3u
a) 6u b) 4u c) 5u d) 3u e) 2u
18. Sobre una recta se ubican los puntos
consecutivos A, B, C y D. Calcular AC, si
se cumple que:
CD
BC
AD
AB
= y además:
9
4
AD
1
AB
1
=
+
a) 4.5 b) 3.5 c) 6 d) 7.5 e) 5
19. Se tiene los puntos consecutivos A, B, C y
D. Calcular la suma de los segmentos AB
y CD, si el segmento AC es igual a 25 cm,
el segmento BD es igual a 31 cm y el
segmento BC es igual a la diferencia de
los segmentos BD y AC.
a) 40 b) 28 c) 36 d) 50 e) 44
20. Sobre una recta se ubican tres puntos
consecutivos A, B y C donde se cumple:
AB = 3(BC) + 2 y AC = 38 cm. Calcular la
medida del segmento BC.
a) 6 b) 7 c) 8 d) 9 e) 10
21. En una línea recta se tienen los puntos
consecutivos A, B, C y D. Si AD=19.4,
BD=13.6 y AC=12, calcular BC.
a) 5 b) 5.8 c) 6 d) 6.2 e) 6.8
22. Sean los puntos colineales y consecutivos
M, N, R y T, tales que: MR(NR) = 11 y
NR = RT. Calcular:
5
MN
MT 2
2
−
a) 7.2 b) 8 c) 8.8 d) 10 e) 12.2
23. Sobre una regla AE de un metro de longi-
tud se colocan las marcas B, C y D, de tal
manera que: AB + CE = 80 cm y AE – DE
= 70 cm. Calcular: BE – CD
a) 40 cm b) 50 cm c) 60 cm
d) 70 cm e) 30 cm
24. Si dividimos un segmento en tres partes,
cuyas medidas son directamente propor-
cionales a 1/3, 1/4 y 1/2, se obtienen
segmentos donde el segundo mide 12 cm.
Hallar la suma del segundo y tercer seg-
mento.
a) 16 cm b) 26 cm c) 36 cm
d) 37 cm e) 20 cm
25. En una línea recta se toman los puntos
consecutivos A, B, C D y E, tal que B es
punto medio de AC y D es punto medio de
BE. Si AE mide 54 u y contiene 9 veces a
BC ¿A qué distancia de A está D?
a) 21 b) 27 c) 30 d) 32 e) 36
26.Sobre una recta se tienen los puntos con-
secutivos A, B, C D y E. Calcular BE, si se
cumple que AC = 3(CD), B es punto medio
de AD y:
2
2
AD
AE DE 289u
4
+ =
a) 13 b) 17 c) 34 d) 6.5 e) 26