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This question group is public and is used in 24 tests.

Author: nsharp1
No. Questions: 6
Created: Dec 10, 2017
Last Modified: 7 years ago

Triangle Proof 2

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Given triangle ABC below, where

$bar{AB} ~= bar{BC}$ , prove that

$ang BAC ~= ang BCA$ .

Isosceles Triangle Height v1

Isosceles Triangle Height v1

$" Statement "$	$" Reason "$
$1. "Draw a line though point B perpendicular to "bar{AC} \ \ \ "$	$1.$
$2. "Label point of intersection D"$	$2. "Two lines intersect at a point"$
$3. angBDA, angBDC " are right angles"$	$3.$
$4.triangle ABD, triangle CBD " are right triangles"$	$4. "Definition right triangles"$
$5. bar{AB} ~= bar{BC}$	$5.$
$6.$	$6. "Reflexive Property"$
$7.$	$7. "HL"$
$8. ang BAC ~= ang BCA$	$8.$

Grade 10 Triangles CCSS: HSG-CO.C.10

A.

What is the missing reason in step 1?

Through any point and a line, there exists one perpendicular line
Assume from diagram
Given
Two points define a line

Grade 10 Triangles CCSS: HSG-CO.C.10

B.

What is the missing reason in step 3?

Assume from diagram
Given
Definition of perpendicular lines
Definition supplementary angles

Grade 10 Triangles CCSS: HSG-CO.C.10

C.

What is the missing reason in step 5?

Definition of isosceles triangle
Given
Assume from diagram
Sides intersecting an altitude of a triangle are congruent

Grade 10 Triangles CCSS: HSG-CO.C.10

D.

What is the missing statement in step 6?

$bar{BD}~=bar{BD}$
$bar{AC}~=bar{AC}$
$bar{BC}~=bar{BC}$
$bar{AB}~=bar{AB}$

Grade 10 Triangles CCSS: HSG-CO.C.10

E.

What is the missing statement in step 7?

$triangle ABD ~= triangle BDC$
$triangle ABD ~= triangle DBC$
$triangle ABD ~= triangle CDB$
$triangle ABD ~= triangle CBD$

Grade 10 Triangles CCSS: HSG-CO.C.10

F.

What is the missing reason in step 8?

Corresponding angles of congruent triangles are congruent
Corresponding angles of similar triangles are congruent
AAA
Definition of congruent angles