Triangle Side Length
Can a triangle have side lengths 3 cm, 4 cm, and 8 cm? Explain why or why not.
No, because 8 is not less than 4 + 3
In a triangle, one exterior angle measures 120°. One of the remote interior angles measures 45°.
What is the measure of the other remote interior angle?
75°
If △ABC≅△DEF, what corresponds with <BCA?
<EFD
List all 5 methods that can prove triangles congruent.
SSS, SAS, ASA, AAS, HL
What are the 2 "Secret Weapons" (hidden parts) that can be used in a proof?
Reflexive and Vertical Angles
Which of the following sets of side lengths could form a triangle?
A. 5 cm, 7 cm, 13 cm
B. 4 cm, 6 cm, 9 cm
C. 2 cm, 2 cm, 5 cm
B. 4 cm, 6 cm, 9 cm
In △ABC triangle △ABC, the two remote interior angles measure 38° and 57°. Find the measure of the exterior angle at the third vertex.
95°
If △ABC≅△QRT, AB = 17, BC = 13, and AC = 12, then which of the following is the length of QT?
12
Given △ABC and △DEF with:
AB=DE , BC=EF, AC=DF
Which method can be used to prove △ABC≅△DEF?
SSS
What do perpendicular lines do?
Perpendicular lines form right angles.
Two sides of a triangle are 7 cm and 10 cm. What is the smallest possible integer length for the third side?
4 cm
In △PQR, the interior angle at vertex R measures 68°, and the exterior angle at vertex Q measures 120°.
Find the measure of the interior angle at Q and the remaining interior angle at P.
Interior Q=60°, Interior P=52°
If △JKL≅△STU, m<K= 45°, m<L= 93°, then which of the following is the measure of <S?
42°
Given △ABC and △DEF with:
AB=DE , <BAC= 90, <EDF= 90, AC=DF
Which method can be used to prove △ABC≅△DEF?
SAS
What is a median?
A median is drawn from a vertex to the midpoint of the opposite side.
Two sides of a triangle are 5.5 cm and 9.2 cm. What is the smallest possible integer length for the third side?
4 cm
In △XYZ, an exterior angle at vertex Z measures (4x+10)°. The two remote interior angles measure (x+20)° and (2x−10)°.
Find the measure of the exterior angle.
10°
If △PQR≅△STU; PQ=2x+7, QR=4x−3, PR=3x+5, TU=9, ST=13, and SU=14. Find the value of x.
3
Given △ABC and △DEF with:
AB=DE , <BAC=<EDF, <BCA=EFD
Which method can be used to prove △ABC≅△DEF?
AAS
What is an altitude?
An altitude is drawn from a vertex perpendicular to the opposite side.
Two sides of a triangle are 3/2 cm and 5/3 cm. What is the range of possible side lengths for the third side?
1/6 < x < 19/6
In a triangle, the exterior angle is 10° more than three times the smaller remote interior angle.
The larger remote interior angle is 20° more than the smaller one.
Find the measure of the exterior angle.
40°
If △PQR≅△STU; in △PQR the largest side is 20. In △STU the largest side is one less than three times the smallest side. The second largest side is five more than twice the smallest side. Determine the lengths of the three sides of △STU.
7, 19, and 20
Given △ABC and △DEF with:
BC=EF , <BAC= 90, <EDF= 90, AC=DF
Which method can be used to prove △ABC≅△DEF?
HL
If BD bisects <ABC, which two parts are congruent?
A. AB≅BC
B. <ADB≅<CDB
C. <ABD≅<DBC
C. <ABD≅<DBC