Triangle Basics
Two angles of a triangle measure 47° and 68°. Find the third angle.
x = 65°
True or False:
Corresponding parts of congruent triangles are congruent.
True
What is true about corresponding angles of similar polygons?
The angles are congruent.
In △ABC, D lies on AB and E lies on AC, with DE ∥ BC. If AD = 4, DB = 6, and AE = 8, what is the length of EC?
EC = 12
What is the sum of the interior angles of a hexagon?
sum = 720°
An exterior angle of a triangle measures 132°. One remote interior angle measures 57°. Find the other remote interior angle.
x = 75°
Name the five triangle congruence postulates.
SSS, SAS, ASA, AAS, HL.
Two similar triangles have corresponding side lengths of 8 and 12. If another side of the smaller triangle is 14, find its corresponding side (x) in the larger triangle.
x = 21
In △ABC, DE ∥ BC. If AD = 9, DB = 6, and EC = 10, what is the length of AE?
AE = 15
What is the measure of one exterior angle of a regular decagon?
one exterior = 36°
Two sides of a triangle measure 8 and 13. What is the range for the possible side lengths of the third side?
5 < x < 21
Two triangles have side lengths 6, 9, and 12, with all three corresponding sides equal. Which theorem proves congruence?
SSS
The corresponding sides of two similar triangles are (x+2) and 18, and 10 and 15. Find x, assuming the listed pairs correspond in that order.
x = 10
In △ABC, DE ∥ BC. If AD = 3x, DB = 8, AE = 15, and EC = 10, what is the value of x?
x = 4
Each interior angle of a regular polygon measures 150°. How many sides does the polygon have?
n = 12
A triangle has angles with measures of (2x + 5)°, (3x − 10)°, and (4x + 5)°. Solve for x.
x = 20
△ABC ≅ △DEF. <A=(3x+12)°, <B=(2x+8)°, and <F=(4x-20)°. What is the value of x?
x = 20
A photograph measuring 8 inches wide and 12 inches tall is enlarged proportionally. If the enlarged photograph is 30 inches tall, what is its new width?
width = 20 in
Three parallel lines intersect two transversals. The intercepted segments on one transversal measure 6 and 9, while the corresponding segments on the other measure (2x + 1) and 10.5. What is the value of x?
x = 3
The sum of the interior angles of a polygon is 1,440°. How many sides does the polygon have?
n = 10
In triangle ABC, the measure of exterior angle A is (5x+10)°. The two remote interior angles measure (2x+15)° and (x+35)°. Solve for x and the exterior angle.
x = 20
Exterior <A = 110°
△ABC ≅ △DEF. AB=(3x + 7), DE=(5x − 11), what is the value of x?
A rectangular poster measures 24 inches wide and 36 inches tall. The poster is reduced using a scale factor of 3/4. What are the dimensions of the new poster?
width = 18 in
length = 27 in
In △ABC, DE ∥ BC. If AD=(2x + 4), DB=(x + 2), AE=(3x + 6), and EC=12, what is the value of x?
x = 6
A convex pentagon has exterior angles that measure (4x)°, (5x + 3)°, (2x + 1)°, (4x + 14)°, and (4x)°. Solve for x.
x = 18